Then the answer is make it mutable.
Make it have the chance to rise and fall as well as take a page from HC 09 and put it per rating and then do like OOTP and put career arcs in the game as well as not have all skills go up/down universally. That would create a variety of career curves, changes in guys, more reasons to follow your players as they evolve along with throwing in realistic uncertainty in all aspects of player development.
That's how games like OOTP can have potential, but not make it fell "scripted" or with there being no risk to a top prospect or a lower-end player never working hard to elevate himself and coming out of nowhere, or have a journeyman vet "click" and he ends up with a solid stretch before retiring, etc.
Injuries had no impact on potential in Madden. Playing well/poorly had no impact (scouts can change their opinions after seeing a guy on the field), it was too stats based for too many of the positions (and in the case of OL, they use "Pancakes"...is that even a tracked stat in real life? Why not use runs/carry to his side of the formation? Sacks allowed? Penalties assessed?)
EA just didn't do it right. That doesn't mean the whole concept of potential is broken.
I don't even care about the real-life player issue. Once a player is in my franchise, like you said, that's it's own world. As long as the progression the player takes is plausible, that's about all that can be expected. Considering rookies still had the same issues, it's a system problem.
The thing I have with the experience thing is that it's still the stats-oriented, except for whatever XP you got in practice (assuming that's not stats-oriented as well). I'm willing to bet that in real life, a player can learn from a bad day just like a good one. In fact a bad day would have more "coachable moments" and the player would get instruction on where he can improve and what to work on.
And sometimes a player's bad day isn't all his fault. HB gets no help from his line and doesn't meet his goals - is that the HB's fault? Is that the HB showing a lack of skills? Football is the ultimate team game, I hope the XP system accounts for that as well.