The purpose of lockout coil is to reject inserted coins if power is off or the credits are at maximum. If you can live without that feature, I suggest disconnecting the coil and zip-tie the armature so that coin mechs work. Keep all parts in place, just cut the coil wire, so that it is easy to put back in working condition again.

Yes Bally games do that and I also like the clicking. But High Speed and other Williams games only release coin lockout when credits are maxed, and maybe in later games at slam tilt - not sure about that, system 3-6 don't.

I guess that's to prevent players being getting mad if they accidentally put a coin in game powered off.

This comes from EM times, when the game at power on was operational but all lights were off until left flipper button was pressed or game started via either start button or coin insertion. Probably to save electricity, this feature was popular at early 70's during energy crisis. There was even a notice inside cabinet, that the location owner should be instructed that he can easily put the game in power save by tapping or kicking bottom of cabinet. A switch then opened circuit to "lock" relay, turning illumination off but leaving the game ready to play (and coin lockout energized, of course!)

Image from Inkochnito's site:

Williams_STD-16A_Important_Notice (resized).jpg