I can't speak for why anyone has or has not mentioned something, but that is standard textbook stuff. As I mentioned, it does not apply to every case, only to tube input stages with zero global feedback - the only type I care about.
In this case your input noise is pretty much just your tube noise, and with that in mind you probably reach for the quietest tube among the readily available ones - the 6922. Its noise resistance is the incredibly low 200 Ohm.
200 Ohm corresponds to noise voltage of .25uV in a 20,000KHz band. And this is what you get when you connect your signal source to one such tube.
In balanced configuration you have two noise sources connected in series, so your noise resistance is now 400 Ohm, with the resulting noise voltage of .35uF - a 3dB increase.
But this is not the end of the story, because the 6922 has two triodes, so you can connect the second one in parallel with the first, for the total noise resistance of just 100 Ohm. That is how you gain 6dB compared to balanced connection.
This is how I I have done it in some of my phono preamps, and the result is incredibly low noise input.
All this is totally separate from the effect of lines, but there are some cases there. One case is long lines, and they do pickup noise, but tube circuits really have no CMRR to speak of, so any hope of a balanced section significantly reducing the common mode noise is way too optimistic. The noise reduction benefit is usually obtained when precisely trimmed instrumentation amplifiers are on the receiving end... or a transformer.
However, this is not our case, as the interconnects between the tape heads and head preamp are usually short.
As result, in the case of my Marantz 7 projects the tape drive used there, the Teac 25-2, has RCA jacks connected to its head, and I use RCA interconnects to send the signal to the active stage. The interconnects are 3' long and there is absolutely no audible pickup in that configuration.
There is also the subject of ground loops... but if everything is done right there will be no ground loops with a floating source, unconnected to anything on its end. Yes, you will have some stray capacitance there, but that is not what causes ground loop.
So no, Charles, the balanced input will not eliminate ground loops, unless it is a transformer input.