The market will stop somebody from doing that. There will be a price that if the bids go above, the bidder will not profit because the required shift leasing rate would not allow the driver to make a profit. If the driver cannot make ANY profit, they will realize quickly and not lease any shifts. The market obviously isnt that perfect, but still, it should protect people from bidding way too high to control the market.
If I completely misinterpreted your main point and instead you are saying that it wouldnt change the way things are currently run in practice, then you are probably right; HOWEVER [and I think this is what the parent comment was getting at], the local governments would be far, far better off, at least allowing for some good to come out of this system
Use a lottery. This is what lotteries are for. Allow only individual drivers to hold medallions, set a price or a profit sharing mechanism between city and drivers, rent medallions for five years instead of selling them, and award them according to a lottery.
A lottery would be terrible for this in my opinion, especially for individual drivers. Who would invest in buying a taxi if they could potentially lose their medallion the following year? Not to mention the rediculous position to put a driver in if he loses the lottery next year and then is forced to find a new form of income. Just imagine the implication for any other profession: tomorrow you may lose the programmer medallion lottery and be forced to learn something completely new from scratch. It would be bad for the industry too since churn would happen randomly vs organically, meaning unecessary amount of "green" new drivers who don't know the streets as well, etc.
If I completely misinterpreted your main point and instead you are saying that it wouldnt change the way things are currently run in practice, then you are probably right; HOWEVER [and I think this is what the parent comment was getting at], the local governments would be far, far better off, at least allowing for some good to come out of this system