There are probably cases where it's rational for a real-estage agent to sell a property before an auction. An auction could well return less money than the other party offered.

I wonder if regulation of the bidding marketplace would make this less likely to happen.

You can write regulations to fix single problems. That comes with a cost. It increases bureaucracy. More forms have to be filled. It's more complex to sell property.

In general I would expect the free market to solve this issue better than a government produced system.