Why yes, having characters that one gets emotionally invested in is the ideal. Unfortunately most games dont have those.
The worst example to me is TES. I mostly just played Morrowind. Oh sure, this character is a Paladin. But he's actually evil. And this is a Necromancer. Hey, he's actually quite nice. Everyone was sort of neutral in that game, everyone was dispassionately grey. Additionally you had no group, so that was even more impersonal and boring.
The game that made me most emotionally invested was Baldurs Gate 2. Namely Imoen, Aerie, and Keldron. To a lesser degree also others, like Minsc and Jaheira. Aerie also has the by far best romance I encountered in any game. Viconia would probably be fun, too, but having an evil character in the party is a true PITA. I did like the evil characters though, they have all been really funny.
Charaters in BG1+2 that have been evil have been really evil, and characters that have been good have been really good, and even the neutral characters had a clear personality.
Despite the fact I didnt liked them much, BG3 actually still has the second best game romance I ever encountered. The "romance" in Knights of the Old Republic was just seven dialogues. I mean I always did it anyway, but it was very superficial compared to Aerie. The "romance" in Neverwinter Nights 2 was one dialogue at the very end. Like ... wtf ?
A story that provides variance definitely provides replayability, so I'm certainly all for that.
