See, it is exactly those characterizations and relationship dynamics between Picard and Vash I dearly love, like Han Solo to Princess Leia Organa or SG1's Vala Mal Doran to Dr. Daniel Jackson. Picard and Vash have a very compelling 'battle of wills' dynamic to their relationship. Vash's brazenness complements Picard's more sedate personality perfectly. She is the ideal foil for Picard's straight man.
Vash breaks into the captain's quarters. Does Picard call security? Does he have her thrown in the brig? No, the good captain beds her and makes her breakfast the next morning. This woman is just too cool!![]()
Yeah, but...
Breaking into the captain's quarters once is cute and romantic. Not so easy to live with day to day, though.

To me "perfect mate" means someone Picard could actually have a long-term relationship with - not merely an affair or fling. I'd say Vash fits into one of the latter two categories. And, just so you'll know that I don't have anything against her, that's probably all she'd want, too. She's not really a long-term relationship kind of gal herself, IMO.