Thanks for the kind words, Dave. I'm never entirely sure anyone actually reads this stuff or cares.
The space cloud is typically—and notably inaccurately—described and depicted, using a water tank or capacitor analogy, as some sort of reservoir or buffer from which electrons are smoothly leaked across the tube at a rate dependent upon the grid's potential. The British name "valve" even suggests this behavior. But that's not exactly how it works. Here's what I worked out by reading through a lot of the ancient tomes and cogitating upon how it works. No guarantees, and a lot of it is handwavy since I'm not a quantum mechanic, only the regular kind that does the electronic equivalent of oil changes, brake pads, and tire rotation.
The space cloud is not a giant tank of noise-free electrons, stored to the point they are permitted to exit through gaps in the grid and transit across the tube, much like a water tank having a spigot at the bottom which releases water at a steady rate. (Even that analogy instantly breaks down, spigot would have issues of laminar vs. turbulent flow because of surface tension, plus other interactions of water molecules with each other, impurities, and the interior surface of the pipe.) If the space cloud were a tank, one might think the electron properties somehow ended up being averaged or muted, analogous to how a capacitor purportedly functions as a shock absorber, absorbing charge in fits and starts but releasing it at a constant rate. (That analogy, too, breaks down, as the capacitor has frequency-dependent behavior, particularly electrolytics, and voltage-dependent behavior, particularly ceramics, and electrons become trapped in the dielectric only to be released over time.) The pool analogy clearly ignores the noise issue. It may help to consider how electrons acquire noise and how it may be removed. Think of how a clean signal is modulated by a noise source, and once having been altered how the only way to make the excrement back into a cow is to extensively filter it and even that isn't perfect, as the filter may itself introduce noise in the pass-band because of ringing in the pass-band or stop-band.
The migrating electrons are modified, one might say "corrupted" since it is a negative outcome, by noise on their journey through the cathode's internal structure and then again as each escapes from the cathode's rough surface. Once emitted each electron—again, containing its own statistical component of the noise spectrum—would normally directly transit across the tube to the plate, except that the interposed grid (when in cutoff or semi-cutoff) forces all of them back into the space cloud, much like a holding pen. So the cloud is chock full of noisy electrons which are attracted to the plate (or screen) but which are not permitted to cross the tube. (The plate is essentially saying, "Give me your huddled noisy electrons yearning to be free, I lift my electro-positivity beside the golden grid", and the grid, decked out in a jet-black Hugo Boss uniform and mirror-polished boots, is saying, "Papers, please!".)
Thermal noise, Brownian noise, flicker noise, mains-frequency and power-line leakage noise from the heater; every possible type of noise is represented in the cloud's electrons. Once noisy the electrons can't become non-noisy without doing work to remove that noise, like using a filter. Even if some averaging could occur, the electrons in the aggregate are all picking up noise on their journey, so it's not like a noise-free source exists to average down the noise.
Shot noise (individual transit) and partition noise (electrons going to the screen instead of the plate, hence "partition"), are different types of noise, being statistical noise arising from how the electrons travel across the tube in randomized discrete units, so that's not the sort of cathode-induced noise we're herein discussing. Emission of electrons from a filament is random, so each electron is a statistically independent event, which is how noise diodes are made.
The cathode's space-charge doesn't have an infinite pool of electrons, which is why high spikes in current demand can damage the cathode as the emission moves from a steady replenishment of the cloud to lighting-bolt like emissions from the surface. The space charge essentially smooths out the electron emissions process, so the electron transit from cathode to plate isn't a random (statistical) process which adds more noise (cf. shot noise or partition noise) as electrons leap from the cathode to the plate, but the cloud does not and cannot smooth out the noise of individual electrons because no mechanism exists for that. A filter is needed. The cloud itself is full of noisy electrons which can't get rid of that noise because that would imply loss of information without some means to do that. It takes energy to move around information aka noise.
All of this becomes clearer, I think, when considering all of this from a different angle: electrons don't actually exist as particles jostling each other in that cloud. Instead, a wave function encodes the entirety of the electron's properties, including energy and noise, and the wave function collapses to actual particle behavior as needed. (Atoms, for that matter, also don't exist. They are just convenient abstractions and shorthand which explain the behavior of the software running on the computer we call the universe.) The aggregate of electrons has statistical noise properties but so do the individual electrons which retain their properties, just in a fragmented way since they're discrete entities. I don't know if this approach clarifies it or makes it worse.
I've rewritten this a number of times and simplfiied the arguments, but it still isn't as clear as I'd like it to be. Time to throw it out into the world.