The directly-heated cathode (meaning that the heater is the cathode) tubes have another advantage: they are nearly instant turn-on, no warm-up needed. Same as vacuum fluorescent displays.
Very old 1920s tubes also used direct cathodes (but used a huge amount of heater power). If you look at the circuits, they had to jump through hoops to have the desired grid to cathode bias while at the same time providing the heater current. I think this would be easier for logic gates: set all of them to ground.
"Very old 1920s tubes also used direct cathodes (but used a huge amount of heater power)."
Yeah, and not-so-old ones too (that is, ones designed in the 1940s). I've a couple of 100TH power triodes whose directly heated thoriated tungsten cathodes consume just over 30 Watts (5V @ 6.3A) yet their plate dissipation is only around 100W. That's pretty miserable efficiency. (They look very pretty when working though.)
You're right about jumping through hoops, circuis become messy and contorted. Also, there's the messy business of eliminating AC filament hum, thus the commonplace practice of using a humdinger circuit on directly-heated triodes such as the 2A3.
Nearly instant turn on can also be a disadvantage when they're used as rectifiers. Tubes like 80, 5Y3G, 5R4G, etc. supply HT long before loading occurs from the indirectly heated ones. In unregulated or poorly designed power supplies it can put additional strain on the PS's electrolytic capacitors.
I've often wondered why rectifiers, especially low power one like those mentioned, remained so popular for so long—or why it took so long for indirectly-heated, unipotential cathode tubes such as the 6X4 to become popular. Cost and ease of manufacturing I suppose.
Reminds me: there are new tubes based on VFD:
https://www.korgnutube.com/en (only 12mW heater power)
Very old 1920s tubes also used direct cathodes (but used a huge amount of heater power). If you look at the circuits, they had to jump through hoops to have the desired grid to cathode bias while at the same time providing the heater current. I think this would be easier for logic gates: set all of them to ground.