the ultimatum card
I don't see why splitting off the authority over certain TLDs, if it could be achieved, would lead to splintering of the Internet in any way. These are only names, which map to IP addresses. The root servers would figure out where to get the authoritative records from, even if some TLDs were administratively under ICANN and others under EUCANN. Splitting the authority doesn't split the network.
That said, it is hard to see how ICANN can be so obtuse on this issue.