There is a term, usually seen in online discussions of games such as Dragon Age or World of Warcraft, known as "character progression". This concerns the development of a character's personal might, be it through the acquisition of more or improved powers (whatever they are), or from the refinement of that character's attributes and skills, as a direct result of gameplay. (This is why level-based systems are dominant; they play directly into the long-established preference for character progression as a central element of game design and play.) For the tabletop role-playing game medium, this cannot be ignored (indeed, it began here), but it can be handled.
The way to address verisimilitude with regard to character progression is to require that the character acquire the new or improved power as a reward for successful pursuit of the character's goals. In other words: progression is treasure, not a leveling-up benefit. A magician must either successfully perform spell research, successfully convince someone with the power to teach/imbue/etc. it unto him, or take it as Spoils of War from an enemy magician. A cyborg must find the bionic component and either trade or steal it, and then find someone or some thing to install it. You get the idea. By this means, the GM can constrain progression to a rate he finds acceptable and he controls what powers a character may acquire. (You can't rebuild your Cyborg into a man-sized Transformer if the technology to do so is not available.)
This also applies to more mundane aspects. The GM controls what skills are available to acquire, and what it takes to learn those skills from said sources. It applies to raw attribute development (usually physical) also; such progression methods requires that the character commit to and devote time to a program of training and study (yes, even for physical development) that they may not be able to do for reasons of more pressing matters requiring their attention. (You can't pick up Electrical Engineering if you're a combatant in the middle of an active military campaign, and you'll not be able to master the Way of the Ennervating Fist if you're already consumed training to master the Strike From All Angles Sword Skill.)
In short, you--as the GM--can, and must, establish what the players can do to progress their characters and then to set what the costs for those improvements are at your table. That is not just one ruling, but a small handful of them that all work together to create the desired effect. A reasonable player will not have an issue with this approach.