The power switch normally is connected to 'hi-voltage' circuits (mains from 115 to 240V AC).
Many manufacturers want to keep those voltages (as far as possible) away from the very sensitive electronic components and audio circuits. (risk of hum)
Some brands (like Yamaha) position the power supply OUTSIDE the keyboards, what means an OPTIONAL power supply..... unbelievable!
Korg, Ketron, Solton, Roland mostly chose for a design with power supplies (including the switch) at the back of the kb's. Perfect solution IMHO.
Does the Tyros ON/OFF switch actually switch the mains, or does it switch the secundary circuits (eg. 12 V) ?
Switching the secundary circuit, implies the voltage transformer always is connected to the mains voltage. (I dislike that !)
Switching on a keyboard is as easy as finding a specific key
Roel