Why don't you wash your hands after using a public bathroom?

Normal people do, Elon.

As a truck driver in the US, depends on the restroom.

More than a few of the restrooms I've visited over the years had no soap or nonfunctional faucets, usually at the smaller truck stops. I started keeping handwashing supplies (separate from my daily hygiene bag) in the driver side cargo hatch of my truck. Access to potable water being often times limited, it would often be hand sanitizer, if I could get it, or windshield washer fluid, sometimes both. Not a great solution, but you work with what you have.

As for the folks that just don't wash, ya, I've no clue.

Disclaimer: I usually wash my hands.

Those that don't wash their hands touch the door handle leaving the restroom. They also likely touch the main door handle leaving the store. If you wash your hands, aren't you undoing it immediately?

I thought about this a lot at my last office I worked at. We had a wide variety of washers, non-washers, religious who also washed their feet (over and under socks), and people who washed and used the paper towel to open the bathroom door but subsequently opened the next door bare handed, and the germophobe who never touched any surface barehanded.

There's no good answer. Though, metal is a pretty bad surface for germs to live on if that helps. My recommendation is to just wash your hands and then try not to think about the rest.

If you wash your hands, aren't you undoing it immediately?
Yup, might as well stop showering too since the cleanliness from showering is also temporary. And might as well not eat anything since hunger is just gonna come back anyway.
My recommendation is to just wash your hands and then try not to think about the rest.
This is the real answer. Don't even think about anything else, just wash your hands every time visiting the restroom and touching anything in there that others you don't know have touched.
Also wash hands every time coming from outside. Just normal sanitary behavior to prevent illness. Hands get very dirty very easily outside. More than we think.
I have a small plastic freezer bag in my pocket, which I use turned inside-out to open the door.
My GF has severe (no, severe) OCD, and among all the rituals that are, objectively, pointless.... This is the one that I wholeheartedly understand and agree with.

I have hand eczema that flares up with harsh soaps. I use hand sanitizer instead, it's small and fits in my pocket. Also I think that some sinks are dirtier than my ass.

Can confirm, I shit in the sinks because they are cleaner than the bathroom and using the faucet as a bidet is gentler than the communist-era 0.25ply (sand)paper.
- same

Because I washed them before using the bathroom, and my weiner is cleaner.

Yuck. Touch the wang => clean your hands, dude.

I avoid this by not peeing on my hand.

I don't think thats the issue, bro. Its touching everyone else's pee the hours since youve last washed your hands.
- If you're doing that, it's good that you're washing your hands.

When I was little I'd run away because the sound of flushing scared me.

If there isn't paper towel I don't bother. No point in washing my hand then touching the dirty door handle.

I have two small hand sanitizer bottles in my pocket, one for unscented soap, the other for unscented hand sanitizer.