FPGAs are a bit piggy on power consumption historically given they've mostly been used for smaller shop engineers prototyping and validating designs from an HDL without needing to use a fab and have not been used in datacenter use cases often. But I'd expect newer FPGAs should be able to turn off power to unused LUTs instead of forcing everything to stay powered on.

Using FPGAs that are massively oversized for the logic they implement makes little sense anyway even if you have a super high pipeline stage count.