Falling Icicle
Adventurer
A skill check in the Basic game without skills, is just an ability check. Simple as that.
You don't need a skill list and you don't need the skill dice (or a skill bonus) to let your PC do something he wants to do in the Basic game: you just say what you want to do, and roll an ability check if needed.
If all you do is have ability checks with no skill dice, then no class is better at anything than any other. Rogues are not better at picking locks than fighters, rangers are no better at tracking than wizards, etc.
Of course that might mean that there are no Skill Tricks for the Rogue. But probably other classes also have something less.
No other class has such a huge portion of its abilities devoted to an optional mechanic like skills. That indicates to me that skill dice are probably not going to be optional at all, at least not for rogues. Otherwise, you have some serious balance issues. Assuming the rogue is balanced with other classes when it has skill tricks, it becomes underpowered if it doesn't have them.
My idea allows people to still use skill dice and leave the rogue unchanged while still keeping things very simple and giving DMs plenty of freedom.