This is one of the reasons SpaceX uses supercooled fuel and oxydizer (and one of the reasons for going methalox in the first place) - the tanks self-pressurize, so they can skip the Helium system.
Pumps are still good because you really don't want the tanks to pressurize at the same pressure as the combustion chamber. If you do, you'll see a rapid disassembly, but your claim on it being unscheduled will be questioned.