Why do so few low power amplifiers using 300B have balanced inputs?

Most 300b amplifiers are single-ended.

Most designers think that there is no point to adding a balanced input to such an amplifier.

But the fact is there is a way to do it (without an input transformer too) that allows the amplifier to process both phases of the balanced signal.

Any single-ended amplifier can be easily modified to do this without changing the character of the amplifier. FWIW, most single-ended designers don't know this is the case.

May I use a female XLR to male RCA adapter at the unbalanced amplifier input?

No. That is the same as single-ended.

In the residential world, you could add an XLR input, and do the same thing, but you won't get any benefit from it unless you actually have a balanced input stage, and even then, whether it's a benefit or not would be debatable. It would involve more circuit complexity.

With the input I described earlier, this is essentially not true. While no SET has a balanced input, they **all** have differential inputs, else the amplifier would be unable to amplify. Try shorting the input grid to the cathode of the input tube and you will see what I mean. The tube amplifies because of what is different between the grid and cathode.

^^ He can, but 5 meters is a long ways to go single-ended, even if the cable is balanced. The adapter, if properly wired, will tie pin 3 to ground. At that point the cable capacitance will increase.

But with a simple mod (which is done by adding a coupling capacitor into the input tube's cathode circuit, which is tied to pin 3 of the XLR, pin 2 being tied to the RCA signal connection) then the balanced preamp can drive the amp directly with no need for an adapter.

The amp at that point will be operating with a differential input. It won't be balanced, but it will work better than with single-ended.