It can, but it's not necessarily the case. If you had a hundred different classes, and one of those classes was Sword Guy, then gaining a level at the end of the session and putting that into the Sword Guy class isn't necessarily different from a class-less system with a hundred skills where you spend one character point to advance your sword skill.
It sounds like it's a presentation issue, but that the presentation feeds into certain assumptions. Players tend to assume that class-based systems keep your character more focused and give you fewer choices, while point-based systems give you more freedom to do whatever, because that's the experience based on so many other games. Gaining a hundred levels in one class might sound boring, since there's no reason to be so granular when the benefits are rigidly codified, but there's a perceived increase in utility of having lots of points when you are expected to spend them on different things.
At the extremes you're suggesting, those classes are just skills, but there still is the other aspects to class & level systems - many of which actually provide multiple skills in clusters or provide skill costs and pools of skill points to spend - and thus the extreme you postulate really looks more like a contrivance to minimalize the difference artificially.
Most class and level improve damage taking when you level up; it's not just "Better at X" but "Better at X,Y, and Z, and able to take more damage"...
Also, class & level systems which have skills usually also have skills limited by level; D20 directly, Rolemaster by max manks at a given level-up, Alternity like rolemaster. Further, packeting of raises
feels different than continuous options to raise.
Some games do push the envelope a little...
Star Frontiers, each skill has multiple subskills at fixed levels by skill level, so they kind of feel class like feel, but they don't affect anything outside the skill's own subskills, and subskills aren't shared amongst the skills, so really aren't classes.
Barbarians of Lemuria is similar in approach, but broader still, and not specifying the subskills.
But L5R is class and level, even tho it's continuous buy - when your insight goes up, you gain new special abilities. Not "Can" but "will"... tho which is based upon what you've trained for.
Alternity punctuates spending, as does Savage Worlds; Alternity, class sets skill costs, and AP's earned only get spent (or saved) when you level. SW, you don't have classes, but have the punctuation (albeit typically once every 2-3 sessions). So it's a skill driven, limited use of character levels.
The experience mode has an equally important feel contribution. Rolemaster's 10K a level feels hard... until you play; each roll averages at least 50 XP...
