It takes pressure in the tank to suppress cavitation in the pumps for rocket engines. It is customary to use helium for most pressurization due to its’ low molecular weight. Unfortunately, it can take a lot of helium in some cases. Some propellants can self pressurize under the right conditions, though here is where the molecular weigh becomes important. O2 with a molecular weight of 32 is eight times the mass of helium at 4.
Heating up the pressurant gas helps considerably, though helium can be heated up as well. Sub-cooling the propellant helps suppress cavitation and allows a lower pressure in the tank to be effectively pumped. I am going to suggest an inducer pump in the tank instead.
If the required pressure in the tank can be reduced from 30 psi or more to 5 or so as the vehicle reaches altitude, the pressurant gas quantity can be reduced by a factor of 6. An electric inducer pump in the tank might make this possible. A pump that is bypassed early in the flight is gradually brought online with increasing power as the tank level drops and with it the head pressure.
The waste heat from the pump can be used on the pressurant gas to reduce the required mass. The pump power can be gradually increased to keep a constant 100 psi or whatever the spec requires to the turbo pumps.
The objections I have had in the past to electric pumps have mostly to do with the mass penalties of the electric motors, and to a much greater extent the battery mass to reach engine pressure. A relatively low pressure pump used as an inducer gets around some of this. If pressurant gas is reduced along with the elimination of their tanks, that should compensate for the all of the motor weight and some of the battery weight. If the batteries are those of the satellite payload, then there might even be a mass savings. Many of the satellite payloads have a considerable amount of their mass in batteries which might as well help haul the freight during launch when they are probably bored anyway.