I've been mulling over the issue of skills and have tried to come up with a solution that will make both sides of the fence "happy".
Instead of characters getting a bonus equal to their level to all skills. Allow characters to pick "skill bundles" at each level. Perhaps a number of them equal to the number of skills they chose at 1st level to train in. Each bundle would consist of 3-4 skills that go together or can be grouped in a way that makes sense.
The skill bundle "Scouting" for example would include Stealth, Survival and Nature.
In this way the player has agency over what skills their character is good at but a number of associated skills will also increase. This is representative of "picking up other skills" as part of your adventuring experience.
Each skill would appear in 2 bundles, with one bundle giving you a full +1 and the other bundle giving you a +0.5. In the case of the +0.5 you don't get the full bonus until you get the +0.5 bonus twice. It would allow for players to actually specialize in a particular skill and other characters won't lag behind too much on untrained skills unless that character has literally never done anything remotely similar to the skill in question.
It's an idea, I'm sure there are problems with it I haven't considered but (to me at least) it seems better than the proposed skill system, while still maintaining some of the "spirit" of it.