I'd love this too, but I think it would need to be performed by a human as an outsourced service. A fair number of opt-out methods are either phone or email only, particularly those where important data is involved (say, bank balances). Even the Web opt-out forms are often buggy and unloved, though perhaps not so buggy that they couldn't be scripted.
I think the only good endgame would be FTC-enforced legislation that data sharing with third parties (except to deliver a requested service) needs to be opt-in. That looks a lot like "Personal data shall be collected for specified, explicit and legitimate purposes…" in GDPR 5(1)(b).
Until a US GDPR equivalent is enacted, or customers stop buying from companies with opt-out data sharing that no reasonable person would opt in to (true of about half of the companies on this site), I think it'll be a sad state of affairs.
