In older games, progression was all predetermined.
So the moment a player was created for the draft, say a 4* player, the game decided the progression of that player. Absolutely nothing you do can change that. If the game decides they were going to top out at 78 overall and never get better, that's it.
With real life prospects, every time you'd make a new GM mode, the game would decide that prospects development path. This is why in one save file you might have a certain 4.5 red player as a 91, and in another they never exceed 78. It has nothing to do with how you deployed or developed the player, the game just happened to choose based on odds/metrics hidden in that player's profile that they were going to become a 91 within x amount of seasons in one save file and were going to become a 78 in x amount of seasons in a different save file.
Players could some times have their stats be altered temporarily for a season or two by playing them well above or below their intended role. In terms of elevating players, it was easier to do with computer generated players who had mutated offensive stats. For example, if you could find a sniper who had a high 70s/low 80s overall but had 95+ O awareness and 95+ wrist shot, in the right scenario they could put up tons of points, and they'd rise to a first liner overall. This would always only last a season and didn't change the fact that player development was pre-determined.
I remember reading a post online where someone had someone gotten into certain elements of a game, and players had something like a "breakout age", along with a development speed.
Why is that relevant to the newer NHL games?
Franchise mode is built on top of the previous gen GM mode. They never rebuilt the mode so it has a lot of the same flaws and bugs such as uneven development (everybody becoming 90+ skaters for example).
While it's possible they've changed this, I don't think they have. Granted, I've played nowhere near enough of this generation of NHL to fully understand the ins and outs of the mode.
I don't think development can be altered, but I think overalls of all players can swing wildly based on the morale system and this is sometimes mistaken for players having an ability to "handle" the development of their prospects. I say this because players don't just go up, they go down as well.