The thermionic effect is very interesting, if the right material is used to coat the cathode then very large emissions can be had. Combinations of oxides such as barium, strontium and others can have both low work functions and high emissions. Currents in the region of over 100A/sq cm can be achieved.

Thus, valves/tubes could be designed to be much smaller and have much smaller currents. For a digital application such as this only a very small cathode current would be needed, this then would mean a much smaller heater could be used.

In the past, miniaturizing vacuum tubes was desirable but wasn't a major priority and further development was stopped when the transistor became available.

That said, in the 1950s portable tube radios were available that used much less heater power than their mains-operated counterparts, for example tubes like the 3V4. It has a directly-heated cathode and a filament/ heater voltage of 1.4V and current of only 100mA (in series mode it operates at 2.8V at only 50mA).