Refusal rights
The problem with being an EIR (entrepreneur-in-residence) is the right of first refusal.
What happens when the VC fund that kept you as their EIR says “yes”?
You can’t exactly shop around for better terms for your hot start-up idea.
And what happens should the VC fund say “no?”
Now you have the opposite problem, the stigma that the VCs didn’t think your idea had merit.