Fixed price allows less flexibility if "gotchas" are found during development, which they almost always are.

But you can get to a middle ground: A large project where I work did fixed price but built in $X hours of additional work to the price, to be used on a discretionary basis when unexpected issues arise. More flexible than pure fixed-price and not as open-ended as costs plus.

Still not perfect: the vendor has every incentive to utilize every last $X hour in the pool, but strong oversight kept the worst of that in check.