Do you think IP rights could work with some kind of exception for independent people who coincidentally happen to invent similar things?

If I'm a big corporation, I see your small company's great idea in the market, and I copy it and undersell you to drive you out of business and steal your market share, you ought to be able to sue me.

But if I'm some dude on the opposite coast who comes up with a similar idea, and I can show documentation of my own independent invention process with notes and prototypes or whatever evidence some court might require to prove that I didn't copy or steal someone else's idea, it would be a shame if I got shut down with a lawsuit. Maybe some middle ground, like what they do with preset copyright royalties for music, ought to exist in that case.