This is a good question and a topic that rears its head pretty regularly in DIY. If we don’t have to work with 300V, we’d all prefer not to; however, there’s a reason that we brave high voltage in our quest for tube audio.
There are a few tubes that will operate reasonably well at low anode voltages —see PDF article here or space-charge tubes like 6GM8– but the majority of tubes are going to want 50V+ on the anode to reach respectable linearity. There is some discussion of this in the write up for the El Estudiante headphone amp.
A triode is unlike the collection of transistors in an opamp; think of it more like a single NPN. Let’s assume simple single-ended operation, too. The more supply voltage you have, the more anode/drain voltage swing you can realize with variations in the grid/gate before you run into current cut-off or out of the transistor saturation region (which is like hitting positive grid voltage on a tube). More supply voltage will allow you to bias the tube/transistor in more linear regions of the transfer curves:
Recall also that tubes pass current in mA so producing usable power (V * I) is going to require lots of voltage (typically hundreds of volts). That high voltage and low current pass through the output transformer to become the low voltage and high current that’s suitable for driving 8 ohm speaker loads.
A lot of it comes down to fundamental construction. Tubes have a vacuum gap across which current must flow, so a decent amount of voltage is needed to create enough potential difference to get electrons moving reliably from cathode to plate. Maximum potential current is limited by the anode voltage according to Child’s Law (three halves power of the anode voltage divided by the squared distance between electrodes). Transistors are a silicon sandwich and capable of much higher current, but they are voltage limited by the breakdown rating of the semiconductor region material/thickness.
Hybrids are a really cool topic, IMO. SS has an advantage in directly driving low impedance loads with high current, while tubes have advantages in small signal voltage amplification (no NFB, high Zin, simple, low noise).
So, can tubes run at low voltage? Some of them do ok for musical instrument applications (eg guitar effects), but usually we want more potential (voltage) to overcome the vacuum gap and get the lazy little electrons moving in order to reduce distortion and achieve good tube-to-tube repeatability.