Would you sell your best startup idea for equity?

Of course - it would make making it a reality - why not!

Sure, idea themself do not have much value, value is all in the implementation. If you find somebody to implement it for you and still give you equity: go for it.

If I don't have the resources or know-how to turn my startup idea into a reality, then why not? Because an idea is just a thought if I don't work on it. And trading it for equity is not a that bad idea, if not worse.