I made a mistake in calling out 'discrete' skills. Really what I was thinking, and mis-described, was systems where the differences are statistically smaller. The archetype I had in mind was D&D, where having a skill typically means a 10% to 20% advantage across the levels at which most people play. But discrete skill systems could of course have more variance, and non-discrete approaches (backgrounds, attribute based, etc.) could be smaller. Apologies. Thanks for the pushback.
FYI, in 3e when playing with point buy stats, the range between "expertise" and actively bad at it at
level 1 can be like from a
-1 (Ability Score at 8) to potentially a
+11 (Ability Score 20; 4 Ranks; +3 from Skill Focus; maybe +2 from Racial Skill Bonus) {I misremembered when I said +15 and was including an instance of aid another and masterwork tools, which you probably cannot afford until level 2}.
Then by
level 3 you're working with a
-1 to a potential whopping
+23 (Ability Score 20; 6 Ranks; +2 Masterwork Tool; +3 from Skill Focus; +2 from another Skill Feat;You can afford to buy (or craft) a +1 Skill boosting item if built by the DMG magic item prices (The Expanded Psionics Handbook has a bunch at +5 and +10 that exactly follow the price formula, and the DMG has a handful as well, and you can , but the published examples are only in +5 or +10); Maybe a +2 Synergy Bonus from another skill; maybe +2 from Racial Skill Bonus).
(That is a player who REALLY wants to be good at that skill, and has invested as much as possible at that level into that one skill, but it is attainable - I have a spreadsheet for this, I use a table based on it to help me when I need to improvise DCs by the tasks at which they are level appropriate or 'theoretically possible to achieve').
And level 3 is certainly "across the levels at which most people play", without getting to the higher-but-not-epic levels at which my campaigns are usually built around (6 to 15). (Those +10 Skill Boost items become affordable (<15% WBL) to craft at level 9. level 12 to buy). {I'm inclined not to allow higher skill boosters than +10 even though the formula covers it, just because there are no comparable out-of-the-book items that give more than a +10.}
(The advancement rate after level 3 slows sharply, but those first three levels quickly give you access to most of the different types of skill bonus and a big chunk of your total attainable bonus by level 20. After that point it's basically just +1/lv in ranks, a skill boosting magic item which eventually caps out at +10, ability score boosting equipment, and tomes of permanent ability score boosting).
I believe 4e also had pretty quickly scaling bonuses for skills, but 4e is not my wheelhouse.
5e and 5e derivatives certainly have smaller differences in capability between characters of course (a significant thing I hated about 5e), but I just wanted to point out that your example doesn't hold across D&Ds, specifically not across the three D&D editions I would choose to play / run (3.0, 3.5, PF1).