A practical implementation of such a system would allow arbitration by the courts, have limitations such as a minimum bid increment (e.g. 10%), etc.
If you can demonstrate that the purchase offer is made because of personal animus, or the buyer has no reasonable and specific plans for the property (i.e. the billionaire buying out a small town without a workable business plan), then the courts would overturn it.
Ultimately, billionaires have lots of ways to mess with someone they don't like. If we don't like that, we should circumscribe what billionaires can do with their power.
And it would still be costly. 10% bid increments is vastly different than today and would lead to property inflation. Going to court is costly. There are plenty of examples of how unfair the courts can be when people with lots of money face off with normal people. It wouldn't have to be billionaires. You could even have private equity abusing the system to manipulate the market in their favor.
You can't submit bids in this system without the intention of buying, if you have the highest bid you're forced to buy.