I'm unsure, the matter seems open to interpretation, what do you think?

Electrolytic capacitors wear out over time with heat hugely accelerating the wear. This is the biggest single cause of equipment failure or poor performance if gear is left on 24/7.
Solid state components do have some mechanisms which, depending on design and manufacturing methods, can cause failure after many hours of use. These are generally "electron migration" effects in which impurities or even intended substances in the manufacturing process can move on an atomic level to cause defects in the device. On the other hand though solid state devices can last almost indefinitely so it's a bit of a lottery and can effect some parts but not others, depending on manufacturer and the process used in construction. We are generally talking many years of use though (20+).
As to switching on and off causing problems for solid state devices that's generally bollocks. Think of a switch mode power supply!.... on and off 100,000 times a second or so!
The bridge rectifier can be stressed by the switch on surge if there is a huge amount of smoothing capacitance and a very large transformer. Soft start circuits are usually fitted in such circumstances though. Tripping of mains circuit breakers at switch on can be a big problem if not fitted. The massive rating of rectifiers for short term overloads usually prevents issues (100 x or so the continuous rating). Fuses will sometimes blow at switch on due to many cycles of heating, expansion and contraction at switch on causing a form of metal fatigue. This is especially common with anti-surge fuses used with a toroidal transformer (toroidals have much bigger switch on surge current than conventional ones). This is pretty much the only time a fuse goes with no other fault being present and replacing the fuse cures the problem... for several years.
Resistors of certain types can be a problem over time. Carbon composition resistors tend to go high over time and especially so if a high voltage is across them. Hence it being so common to find resistors in vintage valve gear that have gone from lets say a marked 100K value to an actual measured 160K!
Other than that there are of course random failures.... parts of whatever type which although well within their ratings and used correctly become faulty for no apparent reason (there really is usually no reason. It's just one of those things). These can be awkward to fix as often the part that's gone is under no suspicion and is only found after all the "usual suspects" have been checked out...

My stuff is all switched off when not in use, except for one of the phono stages which doesn't have a switch. It's better when warmed up and that takes about 20 minutes - something I'm happy to live with.

Do you not use an inrush limiter on your amps now? If not why not, as I'm thinking of fitting one to my BPS,

I switch everything off cos im so paranoid. However im more than happy with how things sound from cold.

I Have changed tact over the years, the amps now I switch off, warm up time is minimal.

Some CD players have large heavy chassis (some amps too) and they do require time to come up to thermal equilibrium and they do sound different until that point. However not many in that category.

The small dac's/pre/phono's/streamers which idle at 0.5w fine I leave them on.

Other wise all off

Yes mine also does, that's why I leave it on all the time. I'm thinking of fitting inrush protection as it gives me the option to take it to someone else's house to let them hear the effect of good balanced power , I took my mother bps to electricbeachs house but I couldn't instal it as he has an old Wylex fuse wire board and it would have tripped that out every time