Yea thought of that.
Here's your three options, basically;
1. New owner can pick what ever budget they want. That puts the existing owners at a disadvantage, as they are held to a $4M swing.
2. Current system, where new owner is held to $10M per with a $4M swing. That puts the new owner at a disadvantage, as they are held to $6M to $14m in all categories (except payroll)
3. Keep the previous owner's budget. This can be a disadvantage if the previous owner is way off what the new owner wants.
Short of giving everybody the ability to pick whatever they want (which, maybe has merit, but I think you'd lose a strategy component to the game), I like 3 best.
-it stops the "don't renew, rebuy the team" strategy to reset the budget/change the stadium
-the budget is probably (granted, not automatically) in line with the current state of the team.
-in my head, it's the most fair of the 3 to all involved.
Now, to be totally above board; the new guy should be able to see the current budget before purchasing the team. I know they can how if the view the league, click on the team, etc etc, but a newbie would probably not know how to access that info.