Here's an even better test for your theory and mine.
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The cash in the system is the culprit. If managers have too much cash, the prices are too high. If many, many managers have too much cash, the prices are too high. If there are fewer managers in the game but they still have too much cash, then prices are still too high. It isn't how many managers there are that matters, it is how much cash they have.
The flaw in your examples is that they make an unspoken assumption that supply is fixed and can not be altered. If no other players are ever going to be created, people will have to spend up to their available resources to acquire the player because there will never be another player available to them again.
But putting that aside, since there's no point in discussing something based on that flawed a premise, what is your solution? If money needs to be drained out of the game when teams leave, are you suggesting that each week, BB deducts additional cash from each team in the game to make sure that the transfer prices stay at whatever fixed point someone deems appropriate?
So do they take this money from everyone? "Hey, new team, I know you're working on building your arena and not spending money on the market, but prices went up 3% this week, so we are deducting $15,000 from your account." Or just from people who want to spend to buy players? "Hey, I know you'd like to buy player X, but prices went up 5%, so we'll take that money from you. On the bright side, he'll cost you less now!" Or maybe just those who sell players? "Player prices went up 5%, because there aren't enough good players. So since you are one of the people making the players, we'll have to make sure to take that 5% out of the transfer fee to keep prices level. Maybe if you'd make enough players, you wouldn't get penalized any more!"
And if that works, all you're doing is reducing the amount of money in terms of pure dollars. Teams will still spend their available dollars on the players, just that those without large reserves built up in the past will be disproportionately affected. Teams who need to spend dollars on arena expansions will be disproportionately affected. And prices for players who are desirable to teams who don't fall into your limitation of having very low money compared to the player's "worth" won't be affected - a 300k valued player would be worth a lot less to new teams if they don't start with 300k, for instance, but if guys with $3M in the bank still want him that price won't drop at all.
Other than all of that, it almost might work. Anything to make sure that you can buy players without people having to actually create them, I suppose.