I have seen rat rods with a semi exposed transmission case above the floor, with no tunnel.
So my question is how hot does the transmission case get?
Thank you, and be well
You may relish the excess heat, the flying parts, the flying gravel, and the noise, [which hasn't been addressed yet], but your wife or girlfriend will NOT. Don't cheap out before you've finished your car, build a floor.
This only my opinion, and should be viewed as such.
I've ridden in a '34 Ford coupe with hemi power and a partial floor with an exposed transmission. It wasn't bad. Wouldn't want to do hundreds of miles a day in it though.