I buy the console mostly for the next games, cross gen or not.
If it has BC it's good plus for me, specially if they are improved with better fps, resolution or loading times. But other than Street Fighter V and maybe a few of these games they will include in that 'some of the best games of the generation' collection for PS+ users I don't think I'll use it a lot for games I already completed.
Maybe more important than that for me will be getting some cross gen games for free in PS5 if I buy the PS4 version. Because I may not buy the console at launch, but I'll get games like Spiderman: Miles Morales or Cyberpunk 2077. So if I buy them for PS4 and I get the PS5 before completing them, I'd like to get the next gen version for free and carry the save.
And well, for people who didn't have a PS4 or only played a few games there, I think it's a great feature because it has a ton of awesome games, many of them exclusive. And now thanks to the PS5 boost mode like in Series X they will run with a better fps (specially in games with unlocked framerate), better resolution (in games that use dynamic resolution) and better loading times (very likely way faster than in Series X).