ZeshinX
Adventurer
I've pondered a house rule that gives character the option to select a new skill proficiency, tool proficiency, or language every 3 levels (starting at 3rd level). This is similar to how 2e granted new nonweapon proficiencies.
I currently use a houserule akin to this. PCs can choose a new skill every 4 levels (4th, 8th, etc). Originally I had it so they got a new skill/tool proficiency when they received an ASI via class, but Fighters being the skill monkeys felt entirely off, so switched it to just every 4 levels for all. Far from perfect, but works well enough.
I find the lack of ability to learn new skills one of 5e's major weaknesses. Sure, you have the Skilled feat, but yeesh. I'm all for simplicity, but 5e's entire skill system leaves a LOT to be desired. Keep the system as it functions, but with a wider array of skills and means to gain them via progression as well. Even 2e, for all its warts, had that option.