I don’t get how anyone could EVER enforce a law or agreement or rule that says something I wrote at home on my device on my time is theirs.
Check your employment terms. I'd wager the first step of that is seeing if you have a paper copy. I know I don't for all the places I've worked or acquisitions I've been through.
Something like an ALCU or Second Amendment Foundation that focused on nothing but that would be a nice-to-have. I think it overall destroys creativity in the industry.

I agree with your sentiment, and that the world should work like your hypothetical.
Lawyers doing lawyer stuff. As to why, you said it:
We'd have to have real lawyers weigh in, but for the most part I think unless you found an undiscovered market then they won't care. Programming isn't unique in the respect that the tools you need to do world-changing work aren't that different between what you might have at home versus a well funded computer science research lab, but you're much more likely to stumble into a marketable app than you are a quicker FFT.