Thanks for sharing your experiences guys, really appreciated.
I was asking because a guy is actually developing for commercial purpose, a version of the Redd 47 (yes, another one... :) and he puts in the front the fact that he developed a special gradual tension rise PSU that is supposed to preserve tubes from "aging". And he highlights this fact as a sort of a must-have option.
There can be amp circuits where a nominal rise time of B+ can cause the output stage valve(s) to conduct heavily whilst coupling caps and other long time-constant paths attain their continuous operating conditions. If the output stage valve cathode is asked to conduct at its current limited capability, and the temperature of that cathode is still rising then plausibly there is stress on the cathode material/surface due to temperature hot spots. I also recall there may be stress situations for screens under certain conditions.
This would be a complex issues to analyse as there are so many different amp circuits, as well as power supply configurations and how fast and at what time they start to raise B+. Perhaps easier to appreciate by just capturing the dynamic start up power dissipation conditions for an output stage valve
Whether a relatively slow B+ rise could reduce any such stress situation is not a direct outcome, and would require justification imho (rather than just advertising blurb).