Leave it on?

There are no absolutes. What someone else does with a different brand of equipment from yours should should have no bearing on what you do. Check with the manufacturer of your equipment and follow their advice.

You don't want to leave a class A amp on.  heat kills.  

Many amps now have a standby feature that keeps the circuit warmed up to the point that the designer thinks is appropriate and ready to go,

Jerry

There is no one size fits all answer. Some equipments turn themselves off after being inactive for a certain period of time (Marantz AV-10), others are just impractical (Class A amplifiers). On the other hand some can stay on and ready without causing any damage to themselves or the environment (Class D amplifiers, DACs etc). Some manufacturers recommend it. Just make sure the equipment is in dark mode (display off), otherwise you might cause display burn in where the characters stick to the display like a watermark even without power (not good for resale value). 

@spenav + 1

I leave my Innous streamer, Technics TT, and PS Audio phono pre, DAC, and power amp ON all of the time (except during thunderstorms). When not in use, I turn off my LTA preamp, and 40-year-old Teac R2R and dbx noise reduction unit OFF.

@maprik From the PS Audio BHK250 user manual, “We recommend leaving the rear panel power switch active at all times but placing the unit in its standby mode when listening has been finished. Standby can be activated by pressing the front panel PS Audio logo button, located on the upper left-hand corner of the BHK Signature front panel. When the logo standby button is not lit, the amplifier is in standby mode, and the vacuum tubes are turned off. Standby mode keeps the solid-state circuitry of the amplifier in a reduced power mode, maintaining excellent performance benefits while consuming little power.”