The American draft system sounds great in theory and it would certainly make things fairer and more competitive but another reason it wouldn't work is the relegation of the bottom three clubs to the lower leagues. It would be pointless for the team that finished 20th to have the most allowance to spend on players as they would be playing in the Championship. Would the highest allowance then go to the team that finished 17th? That wouldn't really make sense..
I think the solution for more parity is a maximum salary cap for the squad each year. This would stop clubs like city being able to stockpile players on ridiculous wages. If you want to make changes to your squad you will need to free up salary space by selling players. It will also mean players will really have to think about whether they want to go somewhere for the challenge or money.
Players can still earn what they want as their is now cap per player but face a decision to either earn the max they can or fit into a good squad. It will really give clubs like city and chelsea a challenge to balance the squad insted of each having 5/6 strikers.
The signing on fee would be a certain % of the transfer fee and free transfer signing on fees also have a maximum.