For thoriated fils there are issues with using DC on the fils... but indirectly heated, no problem.
Actually, some of the very earliest broadcast receivers used tubes with thoriated tungsten filaments, and ran them off DC.
Those were the early sets with the 201-A family of tubes. The '01-A has a 0.25 amp thoriated tungsten filament that runs white hot, almost like a light bulb. It was designed to run off a 6-volt storage battery. The older UV-201's (without the -A suffix) used a pure tungsten filament. They required about one amp per tube. The filament was changed to thoriated tungsten in order to save drain on the battery. Receivers with the older version of the tubes might draw 5 amps from the battery just to run the filaments.
I run the filaments in my mic preamp with regulated DC, as well as my VFO tube filaments. I use an old 12-volt DC 2m CB power supply with a dropping resistor to get the voltage to exactly 6.3. I always had a little residual hum I couldn't get rid of with a.c. on the 12AX7 filaments, and the DC cured it. I run the transmitter VFO tube off the same power supply for the regulation. The VFO uses a Collins type PTO (T-368 master oscillator, highly modified). Even minute changes in a.c. mains voltage would change the filament voltage enough cause the VFO to drift to the point that it was unusable on 40m CW. Since I put it on regulated DC about 15 years ago, it is now rock stable.
I had the same problem with the 75A-4. I now run the whole receiver off a Sola constant voltage transformer. This is a newer model, designed to run a PC in an office environment, rated for just about enough power to run the receiver but not much more. It is very quiet, almost silent, whereas the vast majority of the older Sola CVT's I ever tried vibrated so badly that they sounded like chainsaw running.