How good should the regulated AC/DC power supply filter be in tube headphone amp?
The result of inadequate B+ filtering will be injecting hum into the audio path. I would not expect any symptoms like noise (other than hum which is a type of noise) or reduced tube life.

You need adequate filtering to remove (at least >70-80 dB down) hum from the signal path.  Dunno exactly what is the definition of "high-end tube amp"? That seems rather subjective and "audiophoolish".

Yes you will see all sorts of over-built circuits which are designed on the notion that "more is better" regardless of any engineering principles or any actual measured or perceived performance benefit. The name for this kind of silly behavior is "audiophoolishness".