No, that would really help because it's no different than the cap having a part-percent more capacitance.
Are you sure about that?
The way I am thinking about it is:
The E cap gives back some voltage when it drops to smooth out the DC.
The signal cap would still provide a parallel path to Gnd for other unwanted signals to follow, maybe?
You still remember the formula for capacitive reactance from your tech-time, right? Said at a high-level, reactance gets smaller for any given frequency as capacitance gets bigger, or if frequency goes higher.
In a tube amp power supply, you might increase a 20uF filter cap to 40uF with only a slight perceived change in performance. So would a change from 20uF to 20.047uF really make a difference?
There are reasons audiophile folks want a small cap (0.047uF) to bypass a big filter cap (40uF), but that is to make up for possible imperfections in the big cap, and the performance improvement is often debatable.
The signal cap would still provide a parallel path to Gnd for other unwanted signals to follow, maybe?
A lot of people run into a mental block by thinking "Ground" is some blackhole for unwanted stuff to go down & disappear. It's really just "reference point" or "circuit common".
Back to the decoupling resistor & filter cap. Your schematic has a "210v source" with a series 33kΩ resistor and a 20uF cap to ground. What happens to 1kHz or 100Hz signals applied to your 12AX7 stage, with respect to these components?
The 1kHz signal applied to the 12AX7 grid causes a 1kHz plate current, which is pulled from the 210v source through the plate resistors. Bad stuff can happen if these signal current mix with & are influenced by the current pulled by the 6AQ5 from the power supply due to that same 1kHz signal. We'd like to keep the 12AX7's 1kHz a.c. decoupled from that other stuff to avoid feedback due to a common power supply impedance (as the references talk about).
For 1kHz signal, the 20uF cap looks like:
X
c = 1/(2*∏*f*C)
= 1/(2*∏*1,000Hz*0.000020F)
= 7.96Ω
So that 1kHz signal current sees a 33kΩ path back to the power supply through the series decoupling resistor and a ~8Ω path through the 20uF filter cap back to the 12AX7's cathode resistor. It takes the path of least resistance (or reactance), so that signal current doesn't interact with the bigger currents pulled by the 6AQ5.
For the 100Hz signal case, the 20uF cap looks like:
X
c = 1/(2*∏*f*C)
= 1/(2*∏*100Hz*0.000020F)
= 79.6Ω
Still, the ~80Ω path through the cap is followed rather than the 33kΩ path to the power supply, and undesirable current interaction.
If you use a 0.047uF cap to ground but no series resistor between this node and your bench power supply, the 100Hz signal sees:
X
c = 1/(2*∏*f*C)
= 1/(2*∏*100Hz*0.000000047F)
= 33.8kΩ
So the 100Hz signal current sees ~34kΩ to ground and back to the tube's cathode resistor, while there's only ~0.2Ω of resistance in the wire and back to the bench supply. Interaction with the 6AQ5 signal current is assured, which is fine only as long as the power supply presents a true zero-ohm source impedance. There isn't a regulator or power supply built which can guarantee to do that under every possible condition.
As you get beyond the very basics of amp building & design, you'll find that every part has 2 or 3 different functions it performs. Often people focus only on a single function that they think is most-important. It's easy to overlook some of those other functions, which are equally (or more) important.