Grousing about Levels

Having extensively played Dungeons & Dragons in one form or another – including Empire of the Petal Throne, which is clearly derived from D&D – for more than four decades now, I've pretty well made my peace with its idiosyncrasies. That said, there is one aspect of the game that increasingly vexes me and that's the way that experience points and levels interact with one another. 
One of the first things you'll notice if you take a look at an experience table for any class in any edition of D&D is that, as level increases, so too do hit points. Glancing at other charts indexed to level reveals that nearly every important mechanical feature of a class, such as its combat effectiveness, saving throws, spell and other abilities, likewise increase in step with level increases.  While it's certainly simpler to tie every ability to a character's level, it doesn't make much sense. Logically – to the extent that word has any meaning in this context – abilities ought to go up separately, as a character makes use of them and thereby becomes better at using them or through study and practice. Of course, this is not how D&D works or was ever intended to work. I don't blame the game for not conforming to this specific understanding of experience.
In my House of Worms campaign, which uses Empire of the Petal Throne, this issue has reared its head several times. Unlike D&D, EPT includes a rudimentary skill system that delineates the areas of knowledge a character knows at the start of his career. In addition, as the character gains levels, he has the opportunity to acquire new skills, in addition to the more usual D&D-ish benefits of more hit points, greater combat effectiveness, etc. But what if a character wants to pick up a new skill outside of a level increase? This is an issue, because level increases in EPT occur much more slowly than in D&D. Furthermore, among the possible skills are things like foreign languages that ought to be learnable simply by seeking out a tutor or by spending enough time in a foreign land among native speakers to develop some degree of fluency. (To be fair, this is also an issue in D&D, which ties language acquisition to Intelligence score.)
In my campaign, I allowed characters to acquire new skills (and spells) by spending time and money to study with someone capable of teaching them. This made logical sense to me, since that's how people acquire new skills in the real world. It was also attractive as part of the game, because it immersed the characters further in the setting. If, for example, they wanted to learn the Livyáni language prior to their visit to that far-off land, they'd need to find and hire an NPC to teach them. If one of them wanted to learn the sphere of impermeable quiescence spell, he'd need to visit the Temple of Sárku and cajole one of its sorcerers into instructing him in its intricacies. All of this led to a greater connection to the people and institutions of the setting, which I consider important to the long-term success of the campaign.
But none of this, strictly speaking, is allowed by the game. More to the point, it's contrary to the way skill acquisition is presented in the Empire of the Petal Throne rulebook, which ties it to level advancement, just like hit points or saving throws. Now, obviously, I'm well within my rights as the referee to change anything in the rulebook I want and have done so without any qualms. However, that doesn't change the fact that what I am doing – detaching a level-based ability from levels – is the camel's nose under the tent for uncoupling experience gain, level advancement, and ability improvement. 
I'm by no means opposed to this line of thought. Indeed, I'm rather well disposed toward it, especially of late. At the same time, there's no denying that it inevitably leads to some places I'm not sure Dungeons & Dragons (and games based on its model, like EPT) can go very far. That might explain why I find myself looking longingly at Basic Role-Playing and its descendants for inspiration, even though I am instinctively more inclined toward the D&D approach to most things, given its relative simplicity for newcomers. 
I'd be very interested in hearing others' thoughts on this matter, particularly from those who've wrestled with it in their own campaigns.