In my experience, and apart from components that use Black Gate power supply capacitors, well designed tube gear will be "on song" anywhere from 1/2 an hour to one hour after powering on.
In contrast (in the dark days when I ran solid state amplification), I
heard subtle warm-up differences up to 96 hours after powering up my
amplifiers. Needless to say, I left them on 24 x 7 except during the two month thunderstorm season here in Colorado.
As far as component damage from running 24x7, I agree with the poster who referenced heat damage to electrolytic power supply capacitors. If you reference typical power supply capacitor specifications, you will find lifecycle ratings in the thousands of hours (5-12,000) at a temperature like 105 degrees Celsius.
As far as turn-on surge for tubes, this hotly contested, and most of the mythology stems from applying the good practices that relate to high power transmitting tubes (tubes that operate in the thousands of volts range) to consumer audio devices and guitar amps.
With tube rectification (typical indirectly heated rectifiers like the 5AR4), there's an inherrent delay in the B+ so the tubes come up to operating points gracefully.
Now if the designer uses either a directly heated tube rectifier or a solid state rectifier, all bets are off, and they should have a soft-start/muting circuit to delay the application of B+. If they don't, then they'll stress the tubes each time they power them on.
Cheers,
Thom @ Galibier Design