I feel sorry for Sylvain (it sucks to not be able to read if people genuinely care for you or it's just a way to gain access to resources), but he is also abhorrent for his behavior toward women (even if it is a defense mechanism). His beefs about Fodlan society are justified but he is suuuper privileged within that structure (and in one support, he even acknowledges that his brother had a way worse life. Mercedes?). His behavior is very bratty and reactionary.
I think a lot of his supports are really nice; I really liked Mercedes' because you really get down to what he stands for and she is able to carve back a lot of his nonsense. In many of the other supports, he seems to be incapable of actually being sincere towards women in normal conversation and even when he tries (Lys B support) he fails at it. I think that is why they chose to give him a lot of B supports; he's just not that great at genuine interaction with women because of his poisonous relationship with them. Also, post-timeskip he seems to be fairly depressive and uninterested in much of anything; he is tending that way pre- but he seems even less engaged/motivated post-.
With that being said, I think Edelgard/Sylvain would have been an excellent support because they align so much on core values.
And man does he sparkle in some of his scenes. Even if he's probably faking it.