yeah better a button to start the pump for say 10 minutes or just long
enough to get nice hot water to the tap. with a auto off after X
minutes you wouldnt lose much energy,

best to overinsulate the hot line, like foam around the hot feed and
return the fill the entire stud cavatity with foam or fiberglass
insulation. insulation is cheap, since its a one time expense.

PEX line might be better, being plastic it might not conduct radiate
heat as much