I have a related question.  As a developer, I come up with lots of
ideas.  That's what I get paid for.  My employers do not use every idea
I generate.  They can't.  But if I offer them an idea in good faith, go
through the standard process of submitting it for consideration, and it
isn't used, can I then offer it to another institution (as a freelancer,
on my next job, whatever)?

Bearing in mind that no one can copyright an idea, only the expression
of it.

And bearing in mind that I am not referring to my current employer in
this hypothetical situation.