Anyone have a theory on why some budgets can only be changed +/- 4 each season?
I'm going with the base assumption that HBD is an MLB simulation. As much as possible, the game should model the real-world. Any rules specific to HBD should exist only if they are needed to maintain the game.
If I took over an MLB team, I could cut scouting, medical, training, etc. by up to 100% the next season by firing the entire staff. (In the real world most work contracts are one year.)
So HBD should not limit the amount any of those budgets can be cut.
Raising the budget is different. I probably can't just spend $20M and get a top-flight scouting department in one season. But I could spend $40M and probably get as good of a program as the $20M teams.
IMO, a more realistic rule would be increases can be made up to $4M a year. After that, increases cost 2:1. $2M gets you $1M more in that budget. That would simulate throwing money at top scouts, trainers, etc. to come work for my team. It's going to cost me more to get them to jump ship, but once they work for me I don't have to overpay them to keep them. I just have to pay the market rate.
Besides being more realistic, I think it would solve the issue of a new owner taking over a team with a budget allotment they disagree with. The new owner would be able to cut budgets freely and would have the option of investing (one time) to bump up any budgets they want.