UngeheuerLich
Legend
While I'm not a fan of the 5e skill system as it stands, I'm not in favour of getting rid of it either - characters should have scope for being good at one or two things that you wouldn't expect.
The revision I'd like to see:
Remove the Perform skill and the various musical instrument tool proficiencies. Instead introduce a new category of Performance proficiencies (including those instruments, but also things like dance, song, oratory...). Characters then pick up a number of these, possibly with Bards getting them all.
Remove Deception, Persuasion, and Intimidate skills. Instead introduce a new category of Social proficiencies, each relating to a category of people (nobles, peasants, the military, criminals...). Characters then pick up a number of these - this has the effect of spreading the role of "face" among the party, instead of the high-Cha skilled person dominating the Interaction pillar.
Combine Perception and Investigation into a single skill, and rename it to Senses.
Roll those aspects of Nature dealing with animals into Animal Handling, and the rest into Survival. The distinction isn't really enough to matter.
Add a skill dealing with things like heraldry, social structures, and the like. I think much of this is supposed to fit under History, but that has always felt like a poor fit.
Beef up Medicine so that it's actually worth taking. My suggestion would be that successful use allows the recipient to spend a Hit Die (refresh on Short Rest).
Reintroduce Passive Insight.
Please no passive perception and no passive insight. Just remove them in favour of passive defenses.
This together with the grapple change would pave the way to play a game without skills.