Well, I don't watch much romance anime, because it's conformed to the same damn structures and stereotypes for years and bugs me for probably the same reasons it does you.
I have to admit I like Midori no Hibi, if that even counts, it's a comedy and surreal and if we ignore the manga version of the ending which is still happy for the two main characters, just not for everyone else
then it ends on a high note.
Planetes too has a happy ending that diverges from the manga but it's as rage inspiringly stupid as it is happy, "I know, I'll stop being an asshole and admit I love this chick just long enough to knock her up before I go into space and leave her alone for seven years".
I can think of a few more like this but they're none of them dramas. All shows the main selling points of which are grounded in other genres. They just have plots that centre around a romance.
REC is possibly the only example from the top of my head. Only like 11 10 minute episodes all up but it's backwards. Rather than the two of them being kept apart they fuck in the first episode and the female lead spends the rest of the show trying to get away from the guy. She's still a moe blob though. Tokikake is fantastic and I feel the need to mention it despite it not having the stereotypical GOOD END! It's a satisfying end. Though along similar lines to Planetes
. Millennium Actress too.
Part of the problem is that Japan loves it some fucking melancholy.