Why do you want to "remove" those components?

If you should decide to sell the machine at some future time, the missing parts might be unattractive to a potential buyer/restorer.

In would suggest you consider just unsoldering one wire to the coil and covering the bare wire with electrical tape and twisting the loose section of wire around the other wire. In that way, a future owner could restore the functionality easy enough, if they wanted.

Is there an issue with the slam switch? Typically, one would need to kick or bang the coin door pretty hard before that would end the game. If it is vibrating open occasionally and ending a game when you don't feel it should, just clip or tape it closed.

Cool.
It is your machine and you may do what you like with it.

I do know that as an enthusiast myself, when I find a machine that has had components hacked or completely removed from the machine, I tend to frown and think about restoring the machine to original (maybe not the coin mechs). Thus, if I modify a machine, I usually like to do in a "soft" way where the original design can be restored by someone if they so desire.

The slam switch is not integral to the coin-door lockout coil, other than that is can cut power to the coil and the game. It is there to disable the current game if someone kicks or pounds on the coin door or the front of the machine.

As Stormtrooper points out, the coin-door lockout coil was intended to be energized when the game was powered on. When energized, it moves a rod that moves a mechanism designed to reroute the path of the coin so that it falls onto one of the coin-drop switches (and then into the coin box) and either starts a game or puts credits on the credit unit. When the game is powered off, the mechanism returns to neutral position where the coin path is directed back to the coin return cavity. The intent was to prevent a customer from losing his coin into the coinbox if they accidentally inserted a coin when the game was powered off. That tended to make customers angry where they were more likely to beat on the machine. In home use, the coin-door lockout coil is not necessary and it can tend to buzz if not properly adjusted (and also when it appears to be properly adjusted. Merely disconnecting the wire is a way to mitigate the buzzing and still leave the machine original.