The existing towers can only handle empty ships & boosters. The tower stacks them, then they’re fueled. A catch-only tower would avoid some cladding and the propellant loading lines, but it would still need a deluge system and a QD arm to replace any remaining propellant with inert gas. At that point you might as well pay a little more and get a fully capable tower.

  Starship is designed to achieve reflight of its rocket booster ultimately within an hour after liftoff. The booster returns within ~5 minutes, so the remaining time is reloading propellant and placing a ship on top of the booster. -- Elon Musk