Most players who use skill systems think in terms of abilities adding a bonus to a skill roll, or a skill adding to an ability check, or maybe (as in GURPS) treating the skill as a stand-alone value, with ability scores only setting a default or base level (effectively the same as skill adding to ability.) In such a system, skills are theoretically infinitely improvable.
I tend to think in terms of ability scores as a limit, with skills defining actual competency within that context. If you have average Dexterity and train to be an acrobat, you will be an average acrobat; you will be better than an untrained person, and you will be better than other average acrobats if you've had more experience, but you will never be better than a trained acrobat with high Dexterity.
That's why my "skill system" is "write down how many years you've been an acrobat (or other profession.)" All other things being equal, you will be better at acrobatics than someone with less training. If things are not equal, your training might not matter at all.
I know that's completely antithetical to the way most people run games, but it seems important to me.