Your analysis is flawed.
Unemployed staff reduce their requested salary if they are not hired
This has nothing to do with bidding among teams. If you think this adjustment is important, it can be done regardless. If most teams select a given level, raise the price/salary of that level. And the reverse of course. (I don't think this is necessary anyway)
They might set it too cheap and then everyone will have get the highest level staff - or it will be too expensive and people won't bother getting any staff.
If the economy changes, people will maybe get a level higher or lower than before. It will also depend on the situation of the team. Everybody taking the highest or lowest level? Nonsense.
Consider the hire internally option...
This comparison proves that you don't understand what you are saying. One thing is selecting internal or market. Other thing is selecting the level. Those are two different decisions. If there is no market, you still have to select the level.
If you don't like bidding multiple timea...
This argument is absurd. Imagine a game where, in order to win, you have to stay one hour a day just clicking a button. You would say "that is a crappy game". Then I say, if you don't want to do the clicking, just lose. Nonsense.