Should an audio system be left on at all times?

Kijanki
All 'lectronics is subject to failure. The metal interconnects used in ICs and discrete devices 'moves' under the pressure of the flow of electricity. The break will usually occur when the line goes over an edge, where the metal is thinnest and current density is highest.
When we (my company) introduces a part, especially a new technology/revision, part of the specification includes Lifetime. Parts are put thru a rapid aging cycle while under electrical stress. 1000 hours is typical and an industry standard. There is an accepted rate of failure, usually highest at lower hours.....so-called infant mortality.
That being said, I have never had a SS failure...cap, resistor, I/C, discrete device. My old amp was on as continuously as possible for 20 years. Other stuff switched as needed.
My company makes a line of 'HiRel' and some of our stuff even finds its way into output and power supplies.....and makes full-on class 'd' modules.
Everything has a MTBF, even if it is a HUGE number.
I personally count on Infant Mortality of new equipment. Do a run in for a couple weeks and call it good.

Doesn't current surge, the first 1/2 cycle to saturate a transformer count as stress?

Complex systems fail more often then simple stuff....like hammers. Failures can be simple or complex. Also, complex systems are LESS fault tolerant than simple systems.
Complex, integrated circuits....Pentium is a fine example....
are subject to failures caused by heat and electromigration.
Electromigration is when a conductor 'crawls' under the influence of flowing current. Conductors ALWAYS fail at the point of thinnest metal, usually over a 'step'.