That sounds like a recipe for delays and finger pointing along with massive overruns on the later parts "to fix what those other guys didn't do our way."

If you want separate bidding for separate phases, bid it out that way.

I suspect this would just make all projects much more expensive - bidding for a large project costs a lot of money and can require large teams of people working for extended periods of time. All of that gets paid for out of the projects that are won.

If you now introduce scenarios where projects can have an unknown number of bidding processes all costs will go up to cover the work necessary for multiple companies to prepare bids.

It would just make things much much worse.