Sure it does. You send an email politely reminding them they need to write out a basic reason, and then you get the reason. If they're crazy stubborn and absolutely refuse, small claims court is probably next.
I'm pretty skeptical about the idea of making this a law, but a law could solve the problem.
> I assume you'd also make it illegal for a person to turn down a company without a reason, right?
There's a huge power imbalance here, but okay sure why not? Not many people are turning down job offers after interviewing, but if they do they can spend two minutes writing why.
> How about we make that 6 months in prison.
This strawman is a good way to indicate you didn't spend a single second thinking through the actual implications.