It's interesting, to say the least, that you have listed most of the interspecies relationships in Star Trek.
Actually, I listed most of the ongoing romances begun in serial Trek, period. The fact that most of those relationships are interspecies has nothing to do with why they don’t work.
Spock and Uhura have barely started to have a relationship, so I fail to see how you could already know that it "doesn't work". Jadzia/Worf worked just fine and was quite interesting, IMO, with their different personalities and views. The reason why Worf and Troi didn't work is because it came after years and years of Riker/Troi will-they-won't-they, and because Worf and Troi didn't have as much chemistry (and how long did W/T even last? I'd hardly even call it an ongoing romance). I haven't watched much of Voyager (though I am starting to watch it from the beginning now, so this will change) so I can't say anything about Torres/Paris or Chakotay/Seven, but from what I've heard, wasn't the problem people had with Chakotay/Seven similar to Worf/Troi, it happened suddenly after years of Chakotay/Janeway will-they-won't-they?
I thought Kira/Odo were dealt with very well in season 7 - it certainly wasn't a case of a cheesy "they got together and then they were happy ever after".
In any case, I would much rather see Trek writers have the balls to write ongoing relationships between characters in a mature way, rather than fall back on the tired old cliche of disposable one-episode love interests, or the endless will-they-won't-they relationships that never go anywhere, even though the characters are flirting in every single episode, and there is not really a single good reason why those two just don't get together and get it done with. I always found that annoying in TNG, it makes the show look childish. (Riker/Troi are the best example of how far-fetched the whole thing is, 7 seasons of the show and they can't get together, but when the movies came, the writers decided to have them married - and the only reason for that was obviously that weren't contstrained by the format of a series anymore, so they decided to get it finally done with.)
I can buy that coming from Data or the EMH, both of whom long to be more like the humans who surround them. But not from Odo, who has expressed nothing but contempt for that aspect of humanity. It makes sense that a shapeshifter could mimic a human suffering the pain of an unrequited romantic love, but it doesn’t make sense that Odo would do so.
Odo could also learn to eat and drink if he wanted to, but he didn’t. Every time he was offered food or drink, he told the offerer, with a combination of hostility and pride, that he does not eat or drink. He doesn’t want to learn to copy that human behavior. But he wants to act like a lovesick puppy?
Love, especially unrequited love, is not a simple matter of a biological urge, like eating or drinking, and it does not depend on erogenous zones. He might not have felt sexual desire the way humanoids feel it, but he loved her, and I think could naturally feel a desire to be as close as possible to her, to be intimate with her n any way possible. He might not have thought about it at first - and it is not surprising that Kira never thought Odo would have such thoughts or desires - but seeing her relationship with Bareil and realizing that Kira loved him might have made him jealous, might have made him want to be able to be that close to her.
In Odo's dealings with the female changeling, the complete oneness of the Link is compared favorably to the relatively incomplete and unsatisfying couplings of "solids," so the why of Odo's love for Kira is dealt with directly on more than one occasion. There is no immediate or easy answer.
As for the how of Odo's physical relationship with Kira, it must have seemed like a difficult problem for the writers. It had to be dealt with, but how to do it tastefully? Chimera is the masterful answer to both the how and the why. In the end, Kira and Odo's relationship is about love transcending physical form and appearance: "I want to know you... the way you really are." And later in season 7: "It doesn't matter what you look like."
It has been shown unambiguously that shapeshifters are capable of having sex solids-style when they're in a humanoid form (Odo with the woman he fell in love with in
Simple Investigation, Odo and the Female Changeling in the 6 season episode in which she thanks him for showing her what solids intimacy is like and compares it unfavourably with the great link), so I don't see the problem with
how.
Odo's misanthropy was always partly a mask. After all, he's spent his whole life with the 'solids' and his only real friendships were with them. Naturally, he had a desire to find out more about his own people, but when he did, he was torn about that, too, since they turned out to be what they turned out to be.
There is a very telling moment in one of the episodes (I can't remember for sure but I think it might have been the finale of season 6 when Jadzia and Worf were concerned if they could have children together; I think it might have been during a conversation with Bashir about the subject) that Odo had a very sad/painful look, which revealed that he was concerned that Kira might want a child one day, something he would never be able to give her. There is no indication that Kira ever thought about this or that she even wanted children, but Odo has obviously had thoughts and fears about this. Maybe it even figured in his final decision to leave her and go to the Great Link.