I think I have posted this in here before, but here goes again (possibly). The reason(s) it is a bad idea:
1) As per fanelle's post. Major safety hazard. When contacts close into a fault, they can vaporize, spraying molten silver alloy all around. Trust me, it hurts, A LOT. I have a chest scar from where some from a Size 6 contactor burned through to my breast bone, took almost a year to fully heal.
2) When a contactor coil pulls in the armature, there must be sufficient mechanical force not just to overcome the springs (or in the case of A-B, gravity) and make it move. The MUCH WORSE problem occurs when the contacts hit and current flows. Current flow creates a very strong magnetic field around the conductors in the contactor. The current paths are purposely arranged in a horseshoe fashion so that when you drop OUT the coil, the magnetic forces in that shape are opposing each other and force the contacts open quickly, extinguishing the arc as fast as possible. But when you first close the contactor and the current jumps to 600% of the normal current at that moment, the coil magnet must be strong enough to resist that impulse of magnetic force trying to force them open again. That's why when you get low voltage to a coil, it chatters loudly and destroys the contacts in a matter of seconds. Your finger CANNOT possibly exert that much force on anything above maybe a 20A contactor. That means that what is happening, at a microscopic level, is that when you manually push that "Go" button, the contacts are actually opening and closing 120 times per second. It's only a tiny amount, maybe it only feels like a vibration, but that tiny amount is enough to make the contact material melt and either vaporize, in which case you are killing the contactor life, or cause them to weld, which can be a very bad thing for the machinery.
Whenever someone doubts me, I tell them to disassemble a Size 3 contactor to remove the contacts and covers, put your fingers around the armature, energize the coil and try to hold it from smashing your fingers. Nobody so far has taken me up on that.