> filament is not completely covered by the cathode. The part sticking out obviously has a way lower heat capacity
Something like that. It can also be more/less insulating ceramic around the heater, or heater wire diameter, many things.
> designed to reach their operating temperature faster and hence form a space cloud around the cathode more quickly.
I doubt that, because I never saw a heater/cathode tube warm up much faster or slower whether it "flashed" or not. You certainly saw it a lot in TV and radios, which didn't warm up any faster than the tube manual says. (Heater should stabilize in 11 seconds; some low-current circuits may start to pass small signal in 9 seconds, no big innovation.)
If you NEED a tube to warm up fast, for military urgency, you get a directly heated filimentary cathode. They never totally vanished, for this reason (walkie-talkie, mobile radio, etc)
Blue Glow: WHERE is it???
Various pretty colors on the inside of the glass is normal and utterly harmless. There are always some electrons that miss the Plate and hit the glass. The glass is pure-enough, but not perfectly pure. Many tube glasses have trace amounts of phosphorescent material, and glow blue or purple when electrons hit. In power amp stages, big signal changes the electron pattern and the glow.
But glow between the cathode and plate (where it is also hard to see) is a very bad sign. You almost never see it: by the time this gas-glow is strong enough to see, the vacuum tube has turned into an uncontrolled gas tube and something is melted or smoking. Pretty much: if you can stand there and ask "what is that glow?", and the amp keeps working, then it is probably the harmless kind.
Orange glow inside the cathode is of course normal and essential.
Orange glow on the outside of the plate, on the tubes we use, is overheating. Many power tubes can live with a trace of "color", and big transmitter tubes are sometimes rated to run this way. The plate does not mind, it is a long way from orange to melting. In fact the factory ran the whole tube red hot for minutes or days to drive the gas out of the metal. Cheap modern tubes don't get fully baked, so a little plate glow may liberate more gas than the getter can absorb; back when TungSol made tubes, this didn't happen. Receiving tubes can also get in trouble because their getters work best when warm, not hot; also if the pin-seals get so hot they crack and leak. So you normally do not want to see glow on the plate, but it is not always a panic problem.
> The solution is to drive the tube with a...
It doesn't need a solution. Except in the worst abuse (TV sets with series-strings of low-bid tubes), heater failure is extremely rare. Not counting cheap TV sets, I've seen it just twice: once when I was bored and ran a tube up to 3X rated heater voltage (it lived a while, I had to go 5X to get quick death) and once (frustratingly intermittent) in a 1958 sig-gen that had a very hard life and then got thrown in a dumpster.
Tube heaters are NOT light-bulbs. Receiving tube heaters on hot-start constant-voltage supplies will probably out-live all of us. Any "fix" more complicated than a rugged resistor will actually reduce the box's reliability.
If you "need a solution" for a "military" reason: every time your tube flashes, the enemy shoots at you, then use metal tubes. As far as I can tell, this is why many 1940s glass 6V6 have that black carbon coat on the inside. After the early thrill of having radio, the next fashion was to hide the distracting glow (hard as it is to understand today).