Bankruptcy isn't injecting money into the game, but instead is another hole in the ground, since the only way to reach bankruptcy is through "fixed" expenses (i.e., you can not buy a player if that purchase will put you below zero).
Wrong. A bankrupt team has poured all its money into the economy somewhere. It doesn't much matter where -- the money is in the economy. Then the team simply disappears (with a negative balance) but most of the money remains in the economy. No one goes around removing any of the money it injected into anything except what remained in the team, which was already a negative balance.
If a new team signs up, logs in one time, spends 1k on a trainer with a weekly salary of 100k, and then logs in enough to not be removed for inactivity until they go bankrupt, how does any of that money move the needle one inch on the transfer market? The amount of money available for everyone else to spend on player transfers is literally unchanged, and since the user neither participated in buying or selling players, there is no component of this team's existence that would have influenced the transfer market. Every dollar spent by the team has been thrown down a hole and does not cause the amount of money created from nothingness to consequently increase, nor does it make more or less money be thrown down other holes.
As far as replacement of teams, it depends - there is 500k "added" to the economy, and an amount of money removed if the team being replaced had a net positive balance.
No new team starts with a negative balance, so no money is removed from the economy in the formation of a new team. Rather, there is another $500k in the economy. And I'm talking about the replacement of bankrupt teams. Replacement of solvent teams is another matter altogether.
Overall, the bankruptcy and subsequent replacement with a new team is one factor in the overheated economy. I don't know why it is so important to try to disguise this instead of squarely facing it. How are you ever going to correct the overheated economy if you don't squarely face all of the factors causing it?
How many teams are replaced by bankruptcy as opposed to replaced through inactivity or bans, though? Seeing a team actually even reach the point of their players being transfer listed at $0 for not being able to get back above -500k for two weeks is pretty rare, while teams being replaced because they haven't logged in for a long time is much more common. And those teams can quite often have a fairly substantial bank balance, especially at lower levels where the whole "get a team, log in a few times, disappear" phenomenon primarily occurs - and was exclusive until recent changes in signups allowed new teams to start at higher levels.
Regardless of how many things that may be proposed as a "factor in the overheated economy" (your words), though, the primary factor in transfer prices by an overwhelming margin is supply and demand. Sure, having to pay a week's wages when you fire a staff member may also have some tiny, incidental knock-on effect, but if the market is saturated the prices fall, and if the market can not meet demand, prices rise. If you wish it to be otherwise, feel free to propose a fixed-price system and I'd certainly entertain a discussion on that, though I might not consider it an ideal solution.