...I'm putting myself in the shoes of a person who is in the united states without authorization...and with that in mind, why in the world would I risk exposing myself and my illegal status by participating in something as pointless as voting in US elections...

I just don't see how an average person concerned with being deported is willing to risk exposing themselves by registering with the state government, especially in the last 8 years of ICE really pushing the limits on what they can do.