OK, I didn't really want to talk about this, but I realised that if I accept Whoa Nellie's point of view at Picard and Vash's relationships, I would begin to hate "Captain's Holiday" and "Qpid", and I like these episodes and don't want it.
I want to specify that I amn't P/C shipper, I, if anything, prefer Picard and Darren's affair, though I like the notion about Picard falling in love with his best friend's wife and never telling them both about it. In fact, I would have been even more satisfied if Beverly hadn't learned about it in "Attached" or if they hadn't gotten married, though in the alternate timeline. (Actually, I tried to read Naraht's fanfic, "Attached" alternate version, and wasn't able to go beyond their kiss, because I did feel about it as about Picard's betrayal of Jack.) So I ask Whoa Nellie not to accuse me of some "unfortunate P/C shipper tendencies where they are forced to take Picard or Crusher out of character to make the P/C relationship work."
I, too, believe that "the best fan fiction is always a believable extrapolation from series canon". But I never believe that "in TNG canon, Vash was Picard's main love interest". (Though I don't contend Beverly Crusher, or any other woman, was.)
In my opinion, Picard and Vash's relationships in "Captain's Holiday" consisted of sex, feeling of andventure and mutual double-crossing. As
mon capitaine put it, "holiday fling". Picard told Vash many things about the "Enterprise"'s crew not because of intellectual, emotional and physical intimacy with her, but because he thought they would never meet again. As fellow travellers might confide each in other for the same reason and tell things they wouldn't tell their freinds or family.
[And,
mon capitaine, I think Picard might do Riker impressions as a little private revenge for Riker made the horgon joke upon him.]
We doubt Picard would consider Vash, or ANY woman he had a physical relationship with during the run of the series or the movies as a mere fling. [...] In our opinion to suggest Picard would be so callous about a woman seriously under minds the characterization of Picard as establishes by series canon.
In my opinion, to suggest Picard would be capable for serious feelings (I don't mean there his stroking her cheek, hot sex or things like that) toward the female version of Q* much more contradicts "the characterization of Picard as establishes by series canon" than the "holiday fling" notion about him and Vash.
* [It is canon - Picard (about Q): "He's devious, amoral, unreliable, irresponsible and... and definitely not to be trusted!"
Vash: Remind you of someone you know?
Picard: As a matter of fact, it does.]
I don't think this attitude would be so callous, I think Picard was more callous with Jenice, because the canon implied some intellectual and emotional, if not physical, intimacy of Picard with her, unlike with Vash... And I see the rash abortion of these relationships (through breaking the appointment) as something is much worse than calling a spade a spade... i.e. a "holiday fling" a "holiday fling". Yes, they (Picard and Vash) had a physical relationship (or rather, it had been implied so, because I saw them only kiss, no more)... and what? It is 24th century, and it is Risa... people come there exactly for things like that.
All canon, we admit he was dog in his youth. Which is why we said during the run of the series or the movies.
Picard was 37 when he broke his appointment with Jenice. Not really youth. And there was Miranda Vigo whom Picard had been romantically involved with during shore leave on Earth, in his 49.
And for the run of the series or the movies, in fact, I don't remember any other woman he *for sure* had a physical relationship with in their time. Was it so clear with Darren and Anij?
In my opinion, it was unique case with Vash (because it was only "holiday fling" matter), and Picard-with-other-women-canon isn't really applicable. When Picard said to Nella "I promise you... I'm not one for casual relationships", imho, he meant "serious relationships" with some intellectual and emotional intimacy. (Or he might simply try to look better - should we believe everything people say about themselves?)
You may object that Picard obviously had some feelings for Vash in "Qpid" beyond "hot sex" matter, and I agree he cared about her... but it is canon: in the end of the episode she left him and went away with his enemy... the creature, who was responsible for Picard's most dreadful experience in his life. Of course, he didn't tell her about his assimilation that had happened after their first meeting, so she didn't know about it, unlike his crew.
[About me previous posts' topic... I agree with that you said about different types of intimacy intellectual, emotional, physical, and spiritual. Though I don't agree with your view of Picard with Vash's intimacy, and I *do* think that Picard may (and did) share his feelings with his senior staff, now and again. He said: "I *may not* share my feelings with my crew, but I do have them." "May not", not "do not".
But I agree there were personal feelings and thoughts that he didn't share with any of his senior staff and the certain emotional distance. I think, though, the reason of it isn't his captaincy, but simply his nature... i. e. he would keep this emotional distance not only with his senior officers, but with others as well, even with Vash.

(Though with her Picard's boundary might go in the way different from the way with his crew - he might do Riker impressions before her, but didn't tell about more serious matters... his assimilation, for example.)
When Picard says to Vash: "a Captain does not reveal his personal feelings to his crew", she asked "Is that a Starfleet regulation, or did you make that up yourself?"
And I think the right answer is the second option.

"The captain is a very private man", and I believe the latter isn't a consequence of the former, though may be influnced by it.
And I agree with
mon capitaine:
If he never mentioned Vash to anyone on the ship then I guess it was because he saw it as a holiday fling and as a gentleman he would not seek to 'guyishly' share the intimate details with anyone else.
Vash's affair wasn't important for him as Darren or Kamala ones, so he had no necessity to discuss it, and he isn't a man who talk freely about his intimate life without extreme necessity... in the way Deanna and Beverly do, for example.]
But she left him, going away with Q and he let her go, inspite of his feelings for her.
Actually, I had the draft of my fanfic (not P/C or P/ somebody), where Vash explains to Riker why she went with Q. She said something like that (it is the rough translation):
You know, there is the saying that starship captains married to their ships? But Jean-Luc's case is worse, he married to his duty... his notions about right and wrong. And all his other feelings that don't go along with it is no more than an adultery. He can have these feelings, but he would despise himself for it. He can't tolerate interference of these feelings in his duty... so he lied to me as I lied to him, on Risa. And he was in fury when he had found out my plans about Tagus... breaking of the law aboard his ship! And then there was that Q's game... they were going to kill me, and he ran for my help, alone. It was foolish of him, of course, but... I was able to see his feelings in action, and they were strong as never before - because at that time they agreed with his duty. And after that I can't help saying to Q that he was absolutely wrong, that the game brought out the best in Jean-Luc, his nobility, courage, self-sacrifice, tenderness... I had a glance of what our love could be like, and I realised that it never would be like this, because his duty ever would stand between us... because we couldn't change who we are. And so then I went away with Q.
^ This piece wasn't intended for characterizing Vash in the fanfic, so I don't claim to read her soul... but it is that I think about how "Qpid' developed and changed Picard and Vash relationships from "Captain's Holiday".
I agree with
mon capitaine's words:
she is fundamentally dishonest: she lies and steals and that has got to be a deal-breaker for Picard. Kamala's description of his perfect mate didn't include 'and may steal the family silver at any moment'.
(I don't really care whether all archaeologists behave the way Vash does or no... I know Picard isn't an archaeologist enough for it.) And I can add, having bonded with Picard, Kamala, by her words, have learnt the meaning of duty. I doubt Vash ever learns it. And she said to Picard, in the canon "I cannot change who I am for you or anyone."
So I think all "Risa affair" was only a "holiday fling" for Picard.
Yes, in "Qpid", as Q said, Picard had feelings (mostly negative) about her - like Q or Ardra, Vash had a capability to get under Picard's skin. And yes, he didn't want her die... but as he said to Q, "I would try to save any innocent life, as you know."
In fact, all Q's "point": "they might have been killed. So might you. All for the love of a maid" and all his talk about Picard's weakness and vulnerability are complete nonsense... Picard should reply at it: "A year ago I risked my ship and billions of innocent lives to save *you*. It isn't the love of a maid that made me and my crew vulnerable... It is our humanity" or something like that. But, alas, Picard was too stupid or too noble for it.

But yes, Vash was right in that she said to Q, and Q's game made Picard and Vash closer each to other... and at the same time it separated each from other. Forever. Or the canon says so.