I do not want any change in the rarity of the best players, just the median to be shifted a lot.
That will also affect what people want to train, at least in the long run. First you may think you have a great opportunity to train your new better draftee, then later on you realize pretty much everyone got the same guy - so you actually need to train an even better player to stay competitive. The overall effect is not zero, but I am quite unsure if it achieves the goal either. The goal is to train your own draftees, no?
It's important to consider the overall player supply and demand in most of the draft discussions. You need, say, 12 players per team, each of them having roughly a 12-season career. (Whatever the numbers are, you get the point.) Thus on average you need to get one new player a season to keep refreshing your team. The supply of new players is based on draft and "short-lived" new teams (if they keep playing, then they don't really contribute to the supply but instead just join the overall refreshing cycle). In each league you draft 48 guys a season, while you only really need about 16, right? (The number of bots is irrelevant.) I believe the new teams that stop playing contribute some additional younger players to the market, either by selling (normal transfers or bankruptcy sale) or through free agency (going bot), but I don't know the numbers. Anyway, the number of players needed from the draft is somewhat reduced due to the effect these teams have. Free agency effect is basically the same regardless of the skill levels. In the end, free agents take jobs of drafted players.
So, whether the goal is to make it easier for all teams to concentrate on training their own draftees, or even force them to do so, the overall supply and demand of the players needs to be taken into account. I don't think that even a short-term solution of giving everyone a trainable draftee is really helping, making the draftee level higher will just adjust the requirements most users have for their trainees in the long run.