For 5e I'd like to see NO class be 'the skills guy', and to allow every class to have access to a pretty wide range of skills - perhaps a few default ones which are always appropriate to a class, and then options from an entire list; ditch the pigeonholing via 'class skills'.
The other related thing is to kill this silly dependency on rogues to disarm traps. Let anyone who invests in the appropriate skills disarm them!
You say that so easily, but are there groups that play with no skills? How?
How do you handle success / failure of anything a PC attempts that is not an attack or a spell? Even in very bare-bones dungeoneering, you need at least some form of Perception. How do you make a rogue class without at least Stealth and Thievery?
At the very least, you need an ability score check mechanic, and some basic criterion to decide whether a PC is competent at what he attempts. Think about a Wizard and a Fighter. Even if both have Int 18, the Wizard still knows more about magic, while the Fighter should be better at devising a tactic for a huge battle. Even without skills as a game mechanic, you need a skill system.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.