Why would people treat a rental from you any better
  than one from Hertz?

I don't get tickets in rentals because I assume, as well as my card being charged for the ticket, it'll also be charged a billion-dollar admin fee.

I'm surprised the car got towed or ticketed, whether it was rented from Hertz or GetAround.

Fees only deter people that are conscientious like yourself.

That's why credit cards are a good business even though they give so much free points and the like to their customers.

They bank on the average person's lack of responsibility.

I don't know, to me, I treat Airbnbs and Ubers considerably nicer than respective hotels and taxis because they are real peoples' personal property (I even do the dishes for Airbnb owners even though I'm not supposed to).

I guess I'm in the minority.

Lesson learned.

At what point of sharing does something become unworthy of respect? Is a married couple's property unworthy? A family's? A group of roommates?

I'd suggest: at the point where you start paying for the "sharing" in money.

I have much more respect for something that an actual person owns. If it's some mom and pop bed and breakfast I respect it a lot more than if it is some hotel.

EDIT: After thinking some more it is all boils down to how much the owner cares about it. For example I really care a lot about my car but the rental comapany doesn't really care much about any specific car that they own.

When's it's owned by a publicly traded company.

I guess I should clarify: I put in extra effort to treat them nicer than baseline.

I'm the same way. Granted, I am not a jerk about taking care of my hotel room either, but I definitely think about it differently.

I just know a mistake I make in an Airbnb might mean breaking someones things that have sentimental/personal value whereas a corporate-owned hotel obviously doesn't have that at all.

I think most "normal" people don't mistreat rented cars, so they expect others won't either. It's the same as the original AirBnB pitch. Unfortunately there are added complexities with cars - tourists might not understand local parking rules or road conventions, resulting in towing, tickets and accidents that are not borne out of ill will, they just happen.

Most people may not have mistreated Hydraulix989's car either, but a small minority of them would be sufficient to ruin his car, get it towed a lot of times, etc.

Even if 1 in 10 people mistreat a car, if it's rented out a lot, that adds up to a lot of damage.

You won't believe how detailed and idiot-proof I made my vehicle description (which is a feature GetAround has that's designed for owners to outline parking instructions, etc.).

People just don't read.

Why wouldn't people respect the property of someone else? That's what I don't understand.

you must not understand a great many things then