Is the friction system on a bicycle nesessary?

I’m trying to fix a bike of mine and the friction system on it is pretty barbaric and rusty. The rest of the gear system seems to be working alright. I’m wondering if it’s possible to simply remove the friction part of the gear system.

The bike is a standard road bike.

And to add to it, I’m kind of a minimalist when it comes to bikes, so I’d like as little complications on it as possible.

This is the bike’s gear system at the pedals.

This is what I am asking about removing.

This is the bike’s gear system looks like on the back wheel (sorry for the upside down view).