Yes, but we're a long way down "our hands are off it's ICANN now". The exception might be DNSSEC and the verisign contract continuance. I have no complaint against verisign, far from it: their staff are excellent and they are amazingly diligent and risk averse.
But at a contractual level you could ask is there another company which could tender to operate the root publication function, and meet all stakeholder requirements? And, could that company be legally constituted outside the USA?
Possibly. Ex CERN staff have indicated they were dismayed when the address management function went elsewhere in Europe. I know people both sides of this divide, it's ancient history in some ways.
But at a contractual level you could ask is there another company which could tender to operate the root publication function, and meet all stakeholder requirements? And, could that company be legally constituted outside the USA?