As with all compressed media, resolution takes a backseat to quality of mastering / compression.

I've yet to see a poorly mastered Blu-Ray, and only watched a couple Blu-Ray 4k discs, but online streams at 1080p or 4k are sometimes rather bitstarved so...

With DVDs, some, perhaps many look just fine on a larger screen, but there are some whose mastering is very poor, and those will look really bad on a larger screen. My copy of Forest Gump features closeups where the characters face translates around on their head. But most of the other DVDs I've watched are fine. Yes, Blu-Ray would be better, but not so much that its worth rebuying.