I guarantee that ANY electronics will have a much higher failure rate when turned On/Off vs leaving it on.
Your guarantee is a considerable over-generalization at best.
For starters, your guarantee totally ignores how often the equipment is turned on and off, how long it is left on when it is on, and how long it is left off when it is off. Your guarantee also evidently extrapolates from your experiences with certain equipment to all other possible equipment designs, part qualities, usage patterns, and environments, which is, to use your term, "bs".
All electronic and electromechanical parts, whether resistor, capacitor, inductor, transistor, analog integrated circuit, digital integrated circuit, relay, even printed circuit boards, have finite MTBF's (mean time between failure) if left on all the time. The MTBF is typically non-linear with the age of the component (i.e., older components fail more frequently). New components also fail more frequently, especially if they are not adequately screened and burned in by the manufacturer. As has been noted in some of the posts above, MTBF is typically temperature dependent, and will be shortened as operating temperatures increase. It will also typically be shortened due to the thermal stress of being powered up and powered down repeatedly, which is apparently a key basis of your statements.
As I indicated in my earlier post, an analysis that would balance and combine all of these factors for all of the parts in a piece of equipment, and define an optimum power-up/power-down duty cycle for even one specific design, is essentially an impossible task. Most of the responses above, including yours, are based on perspectives that just address a limited number of these factors, for a limited number of part types in a limited number of designs, and understandably don't present any quantitative trade offs.
As I said in my earlier post, as an experienced electronics design engineer I believe that the best approach (for solid state gear) is simply the common sense one of turning the system off if you don't use it frequently, and leaving it on if you do. If like many of us you are somewhere in the middle, and use the system neither very frequently nor very infrequently, then you won't be going very far wrong with either approach.
Regards,
-- Al