Sealing air leaks by replacing loose duct tape would increase the efficiency of the system and increase its output over what it had been.
You may have felt that the air delivery of the system was normal, but it was probably degraded and the work you did may have brought it closer to the original design.
Duct tape? In my home (2019) they used a tape, but then coated it in some sort of liquid polymer that hardens... I've seen the aluminum tape used on RVs and it *****... But I agree, sure.. more fan could cause that.
mastic is often used to seal ducts, along with a mesh tape that is similar to drywall tape. Duct "tape" is not legal in many places to use on ductwork.