At the very least it would make people more serious about locking them.

Sounds like paradise for lock pickers without moral fiber (actual pickers tend to have good rules they abide by) and desire to monetize their hobby.

“Oh yeah, door was wide open, I swear!”

Can we extend this a bit so that if you’re walking through a park at night, mugging you is kosher?

Can we extend this a bit so that if you design and build a house without a roof and you're wet when it rains it's the building company and construction code's fault?

No, but it’s good to know that if you’re careless, tired, sick, etc... I have free reign to rob you blind.

In United States law, trespassing is often still trespassing, even when the door is open