"potential" was introduced at the start of season 5 (1-1/2 seasons ago). Existing players were given an "All Star*" potential, with the asterisk indicating these existing players, so there is not much experience with the actual impact of the potential limits.
Potential has been described as a soft cap, which while not preventing improvement, creates resistance. It would be reasonable when the soft cap was first encountered that training would only be slowed down a small amount (say 5%) so it might be that that players with the extreme lowest potentials might be slowed a bit, but not being noticed, and perhaps when you training him another 3 levels that there would be much greater slowdown.
Also potential has been indicated to slow the overall improvement based on a combination of skills, rather than being a limit on each skills. This could mean that you could develop a player in different ways before being slowed down. Depending on how it is implemented, it might mean that you will see different slowdowns based on the combination of skills and what you are training.