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.
I can safely predict that the odds of teams investing 40k/week in scouting the draft as a result of this proposal is approximately zero. The draft is a whole different beast and certainly something that could also use some sprucing up, but as it stands there's no reason to invest much money into it.
I also don't think that tanking is generally done specifically because people want to be able to train. At some point in the erosion process, a team reaches a point where continued progress isn't sustainable and then it makes sense to do a refresh of the team's roster. I hit that a few seasons back, and so I guess for a couple of seasons I was technically a dirty tanker myself. Most of the time, the tanking option is taken for people who don't feel like they can compete at a higher level without a financial advantage, which is an opinion that often is self fulfilling.