Thoughts on using a smart plug on intergrated amp.

This plug will not affect your listening pleasure.

Cheers,

1. There are three points to consider.  
2. Many integrated, pre, and power amps have electronic power supply protection circuits and/or software system checks on startup. Depending on the circuit or software design, leaving the power switch on and using a smart plug my bypass these failsafe designs.  I would contact the manufacturer in this regard to assure long term reliability will  affected, or if there is potential for surge damage.  
3. +1 @ghdprentice Electromagnetic interferes, which includes radio frequency interference will enter at the weakest point causing distortion.  Assuming the smart plug has chips (timer, blue tooth, IR, or WIFi) it mat be an RF generator.  This may cause distortion called digital glare in the press.  An OTS smart plug may also affect AC power transmission limiting dynamics  Therefore, SQ may be affected.  
4. +1 @jeffbij The best solution is to use another component with a remote like a DAC or disc player with a trigger connection, assuming your integrated amp has a trigger.  The trigger technology is old, so I would assume it has one.  The trigger circuit in your integrated amp should be designed to not bypass the power supply protection circuits or software system checks.  Check with the manufacturer. 

In conclusion, check with the manufacturer on ​​​​​​​1+ 3.   Test SQ on any solution.   Use good quality audiophile electrical connections, interconnects and cords in any solution you use.   Good luck  

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I use one of these SwitchBot Button Pushers my tube amp to make it "smart" and give it remote control/auto abilities. It presses the power button on the front of the amp for me.

I would approach with caution, most smart plugs are not meant for high amp circuits.
 

If you absolutely must, buy only from a reputable brand from an authorized dealer. I.E Schneider from Digikey or Mouser.

Do not buy from Amazon, even if it from the manufacturers store. Amazon, especially the market place, is full of fake items that are near impossible to identify until after they set your house on fire (yes, it does happen). Fake items get returned and mixed in with genuine items frequently.

The internet is full of bad advice, and none more than for electrical equipment. The advice is often surrounded by phrases like "I have been doing this for years and never had a problem." Random Chinese stuff needs to be de-rated by about 80% (yes, they are that bad), so a 20amp random Chinese outlet is really a 4amp outlet. Your outlet should exceed the fuse rating on the amp by more than 20%, so a 4amp fuse requires a 4.8amp outlet (preferably much more). Use a reputable North American or European brand that is UL listed from an authorized dealer. Also, be wary of IoT devices in general, there was a recent report of wifi enabled vacuum cleaners purchased on Amazon that were sending telemetry back to Chinese servers.

Two good suggestions so far are to use a remote controlled button pusher or an extra device with a signal wire. This could also be easily done with a Raspberry Pi with all the goodness of a smart device and none of the worry of your bedroom activity being sent to a server overseas.

Another good suggestion is a remote controlled outlet, these use either a relay or or a solid state relay. They plug into your standard outlet, but are designed for high amperage. Schneider makes one that is WiFi capable, there are also remote controlled devices used for fans and dust collectors.

Lastly, you could use a solid state timer. I use one to turn on my espresso maker, and love it.

Personally, I would not put a wifi enabled plug on my main system, but would seriously consider it on the system in my shop or basement. 

Set an alarm on your phone. Get up, turn off your amp, go to bed.