I, for one, find any system where money is the only thing that talks to free agents unrealistic and difficult to manage.  Years ago, I ran simulation hockey leagues, and I balanced three factors that a player used to determine where they will sign:  Proposed (promised) playing time on their new team, how good the new team is, and how much money the offer was.   Some players were 60% about money, others were 0% about money, and each had their own 'personalities' to determine who only cared about cash and who just wanted a chance to win.

I believe more factors should be included in players decisions to resign, or sign with a new team.  You currently don't get 'hometown discounts' or players who care if they'll play or not (I could sign a guy at a max contract that's clearly my number two catcher, and he'll still take my bid over someone offering $1 less.)

Players should have 'personality' ratings that ecompass their career goals/desires, that may shift with time.

Winning:  How much does a player care about winning?  High players in this rating won't resign with losing teams, and will take less money to be on winning teams.  Low players in this rating will not take a team's record into their decision making.  This rating would likely shift up over time if a player doesn't get a ring, and may go down after a player gets a ring (in some cases).

Role:  Players high in the role category are willing to contribute to a team in any way possible, be that a platoon 2B, a great pinch hitter, or even be more content in the minor leagues.  Players low in the role rating want to be featured in the starting lineup, bat 3, 4 or 5, or will not resign/sign with a team, and would be more likely to retire if only a minor leaguer.

Greed:  Players high in this rating simply want to get paid.  These players would leave quicker if going through arbitration every season, be unlikely to resign mid-season without a HUGE contract, and go to the highest bidder in free agency.  Players low in this rating consider other factors over money in resigning and signing.

Loyalty:  Players high in the loyalty rating are more likely to resign with a team, and more likely to sign as a free agent with previous teams.  This rating would go up each season a player remains on a team, and take a small hit when they are traded/added to a new team.  Low loyalty players may not even offer a bonus to previous teams in free agency.

Modify the temper rating:  The temper rating would also apply to players looking to hold out, complain, or not play as hard if they are not having their needs above met.

I understand that this is a large change to the system.  I feel that this would be a great change to the game, in creating more diverse player personalities, drafting strategies, free agent decisions and roster management.

Winning:  How much does a player care about winning?  High players in this rating won't resign with losing teams, and will take less money to be on winning teams.  Low players in this rating will not take a team's record into their decision making.  This rating would likely shift up over time if a player doesn't get a ring, and may go down after a player gets a ring (in some cases).

How would this help the losing teams that are trying to improve?  Wouldn't this actually widen the gap between the good teams and the bad teams?

If the ratings are randomized evenly, no.  There would only be a handful of players high enough on the winning scale that would reject lower teams.  Outside of random numbers gone wrong, that shouldn't mean all of those guys are high end free agents.

There's a full day dedicated to budgeting, and there's strategy in setting your budget year to year

With some shades of grey in between, basically there are two camps; people that build using the draft and IFA system and who invest in that, and people who spend on payroll.

You are basically proposing to eliminate the latter. Why would I have $125M in payroll if some random event other than the power of my bucks says "screw you Charlie, you outbid team X, but they won the lottery?"

I say that as a guy that does not have nor probably never will have payroll over $90M, so it's not protecting my own self interest.