The current bonding process works kinda like car insurance, while you own a well you pay a monthly premium that covers the well to some level. When you sell a well coverage ends and you stop paying for it.
You have to be bonded to buy a well, so the bond burden transfers when ownership is severed.
So a well might have several different bonding companies over the course of it's life.
Any one who has operated that well can be held liable for it, but companies won't bond you for a well you don't own. Active operators that are permitting wells want to be on good terms with the state will agree to pay for a well if asked. This has happened several times at companies I've worked at. Plugging typically is like $50-120k, when you're drilling 300MM of wells a year plugging have a dozen wells here or there to stay on good terms with the state is a no brainer.
The problem, I imagine is there are/were a lot of fly by night companies drilling shallow wells for pennies that didn't plug them properly or just left them shut-in.
A modern HZ well might cost $5MM to $15MM to drill, apple to donuts with a well drilled in 1935 for $300 well with equipment delivered to the site by horses. My suspicion is that there are very few of the abandoned wells are horizontal. Most are these small cheap conventional wells.
Spindletop was over 120 years ago...
Two points being, not sure how you would have to change the current process, and then if that's even necessary are we are mostly dealing with wells drilled generations ago.