Likewise, the only handwriting for better impression I have seen was in stuff like love letter. It could possibly done also in super high formal situation (diplomacy, school diploma) or some such, but otherwise it was not a thing.
Relevant for this conversation, dot matrix printouts were considered "cheap", and people were warned not to submit dot-matrix printouts for things like job applications, formal correspondence, etc.
If you were a kid and you tried to hand in a word processed/printed essay in school, even into the early '90s sometimes, you'd get pushback that's very similar to the AI pushback of today. "How do I know YOU wrote it?", "The computer is doing the work for you". They'd force you to rewrite it, properly, in pen.
Handwritten pages always signify special care, indeed as you say that’s why you see that in diplomas and such. There was a time when I kept hand written letters going for my close college friends, on good stationary. I think we are just in different situations/places/demographics.
[edit] also I kept my job application rejections (paper mail). These were very instructive as they showed a pattern of rote rejection that made me less discouraged.