Subframe connectors for a driver/cruiser, necessary to weld to floor?

I was thinking I would buy the steel 2x2 and fabricate them, just welding the ends to the subframes. My question is really whether or not welding to the subframe without welding to the floor makes sense.

I’m honestly not going to remove all of the undercoating and my interior, but I would like to add some strength.
That will work very well. I did that 2 x 2 square tube without weld to floor. I drag race the car w slicks and 408 and no harm to body.