I would think that was to keep players from beating on the cabinet to increase the score to win credits. however, I could be wrong. really don't know for sure

Cheap shock mounts.

Good question, and I'd say a very plausible explanation on your part.

Hi
for "to hinder increasing the score by beating": Shouldn't the grommets be mounted underneath the relays ?
The "points relays" are HEAVILY used throughout the game(s) - How about: The grommets are used the same way as Locking-nuts are used ? (these relays will never get loose due to vibration) Greetings Rolf

Lottza gud possibilities here!
I would have to side with Dirt on this one, relays are noisy and loud. and the score relays hammer the entire game.
I see those on lots of machines. and they are all dried out and shrunk/fallin appart.
I have used mouse pads cut and drilled to replace them. todays gromets I believe are too stiff to do much sound dampening.
Now, the question, "do I need them?".
Well, there needs to be something there, the holes are larger to hold them in.
How noisy is your game room? would it matter that much not havin them?
you decide.

I've bought these from Marco's. My Flipper Parade (1961) has them in many places, including under the bulb holders for the score reel illumination. A bit of a trick to squeeze the new ones into the holes, but I find that using a thin paintbrush handle to squash it through helps.

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PBR sells black grommets.