Uneven cath wear may be an issue with a direct-heated power triode, but not on a low-po indirect-heated tube.
No, but if one tube is at (say) 300mA @ 6.3V and the other at 400mA @ 6.3V, what is the result in series connection? Note that the heater is a tungsten filament with a temperature dependent resistance.
The tube that would like to get more current, will not get hot enough, so it's resistance will end up lower, which will make it's heater even colder and the one in the second tube even hotter.
Can you smell a potential "race condition" where one tube gets colder and colder and the other hotter and hotter? Where does it balance out.
Anyway, making the heater voltage balanced (referenced to what?) does not change anything to the supposed cathode wear, since the voltage gradient from one end to the other is the same.
I was merely talking about heaters designed to be driven by constant voltage (low source impedance) because they will stabilise this way in series.
In my experience, however, they do it accurately enough (at least if they are from the same manufacturer).
Yes. USUALLY it will work in practice.
Except when it doesn't.

[EDIT to add: Does it matter if one heater in a string is 6.1V and one is 6.5V?]
Depends. The problem heater resistance is non-constant with temperature, heater power will depend on voltage and more voltage will make the filament hotter, raising it's resistance further while the second filament with less power will run colder and will thus have a lower filament resistance which in turn will mean it's resistance will be lower.
It is really a question of how big the actual variations are.
But, would you (for arguments sake) connect a 25W and 50W 6V light bulb (tungsten filament) in series and power them from 12V, because it is after all 6V+6V?
1/4 of HT, which is midway between the cathodes in a SRPP or WCF. That’s for minimizing stress between heater and cathode, rather than the (alleviated) concern about uneven heater wear.
Usually not a good idea with AC heaters (I know we are talking DC heaters here, but I thought I mention it). And normally even phono stages and microphone preamplifiers are fine with AC heaters IF they are constructed correctly.
Bottom line, run parallel filament tubes parallel, not series.
If that causes very high currents, you can always split heaters into multiple circuits, it is generally harmless.
Use AC where you can, tubes are designed that way.
Make sure to reverse-bias the parasitic cathode/heater diode which is what usually causes hum with AC heaters, even if correctly symmetric heaters.
If you must build totem poles using tubes, use a separate envelope and heater voltage for the upper tube, EXCEPT where your tube was explicitly designed to have significant opposite direction voltages. Often PCC tubes have heater structures more suited to such a setup and often it is specified if a tube needs to be in a specific position in the string.
Thor