People have gotten the weird idea that somehow the filament of the 45, the 2A3, the 300B, and the 845 are responsible for the ultra-low distortion, and the super-vivid tone color, of the DHT family. Wrong. It isn’t.
It’s the grid. DHT’s have a physically large grid, well spaced away from the whirling cloud of electrons called a "space charge". Surprisingly, electrons are not directly emitted, pass through the grid, then strike the plate. Instead, they whirl around in the space charge, find a passage through the venetian-bland repelling field of the grid, and are accelerated to the plate.
It’s the grid geometry that sets not only the DC characteristics of the tube, but also its linearity (especially high-order terms). This is the most critical part of the entire circuit. If you need pentode or beam tetrode characteristics, fine, you’ll have very low Miller capacitance, very high output impedance, and easy drive characteristics. This makes an excellent RF modulator, where distortion doesn’t matter.
But if low distortion comes first, and you’re not asking for 20 to 50 dB of feedback to linearize the whole amplifier, a true purpose-made triode should have the lowest distortion. Since there are already lots of octal sockets in PP power amps, why not make a special triode tube just for them? There is some design work to optimize the grid structure so DC biasing is the same as a triode-connected pentode, but the absence of all those other grid wires should help. If the design is good enough, it could rival the 300B without the hassle of direct heating and the complex filament circuit.