What you're describing isn't a cost plus contract, it's a fixed cost contract for a study (assuming cost/hour is fixed). These exist, they're frequently a good idea.
Cost plus would be "deliver a FTL ship, we'll pay you X * costs, no it doesn't really matter if you go 10x over what you initially quoted us for the work and still don't have the thing". You can see why contractors under that model are willing to make unrealistic quotes and promises about FTL, or for a real world example why SLS is many years and many billions of dollars behind schedule.
Cost plus would be "deliver a FTL ship, we'll pay you X * costs, no it doesn't really matter if you go 10x over what you initially quoted us for the work and still don't have the thing". You can see why contractors under that model are willing to make unrealistic quotes and promises about FTL, or for a real world example why SLS is many years and many billions of dollars behind schedule.