Here is a quote from the Wikipedia article "Vacuum Tube."
"Tubes on standby for long periods, with heater voltage applied, may develop high cathode interface resistance and display poor emission characteristics. This effect occurred especially in pulse and digital circuits, where tubes had no plate current flowing for extended times. Tubes designed specifically for this mode of operation were made".
Here is a quote from SM0AOM at
amps@contesting.com, June 2003.
"On the other hand, the filament hours obtained on 4CX250B's in the Standard Radio ST1610 ship's transmitters usually were less than 8000 when the transmitters were used for automatic radiotelex service. A lot of effort was spent to find the causes, and poor filament voltage regulation together with long intervals of stand-by without plate current was deemed to be the culprit."
Here is a quote from the UK Vintage Radio Repair and Restoration website August 9, 2010.
"The Brimar Valve and Cathode Ray Manual No 10 says they made two sorts of special quality valves, ruggedised valves designed to cope with shock and vibe and Other Special Quality Valves ruggedised but also with a special cathode tube alloy designed to prevent the growth of a resistive layer between the metal cathode tube and its emissive surface. It says this layer was especially likely to form when valves were run with very low cathode current or in cut-off condition for long periods.
Some of these Other SQ valves were recommended for use in computers. Examples include the 7032 heptode, and E88CC, 7489 and 7492 double triodes."
My comments again...
For the vacuum tube computers this was a problem and special tubes were designed. Some of these are listed in the RCA Tube Manual. When I worked in the TWT industry this was a problem for customers who would keep their TWT amps in standby most of the time. A bit of time drawing cathode current would fix the problem. As far as I know this problem occurs with oxide cathodes and not thoriated tungsten cathodes. The 4CX250B's mentioned by SM0AOM have oxide cathodes.
In any event cathode depletion will occur as least as fast with the tube in standby as in transmit because cathode depletion is due to the electron emitting cathode material evaporating.
So, the original question is how damaging is long idle (standby time)? Since it is not a well known phenomenom to amateur radio operators I would say it is not very damagine.