So if, instead, anyone would be trainable at any position each week, that just means that training will no longer be a choice or a cost-benefit decision, just a default "everyone does it" option. It will significantly slow down the erosion that causes higher level teams to eventually have to come back to the pack, and basically the richest teams will buy the best trainees and be able to custom-build the best new players while still competing full-bore with the best current players.
The main reasons teams sell the best trainees is because 1) they bring in lots of cash which is necessary to compete in the overheated transfer market and 2) because it takes years to fully train a player and they may not be competitive while doing so.
More likely what would happen if all teams from D.I down to D.IV would prioritize training under this suggestion is:
1) Most teams would spend the full $40k per week on scouting because now it's easier to train.
2) With more players being trained, more teams would spend on Level 5+ trainers to maximize training speed.
3) Teams would spend on acquiring better or retaining existing higher salary players since they could now train players without sacrificing competitiveness.
4) Team salaries would eventually be higher as teams carry a starting lineup and a trainee lineup.
All of those would take more money out of the game and, eventually, might even eliminate the need for the luxury tax. Tanking might even decrease since teams could now train players without sacrificing competitiveness.