It's not just that it doesn't "have a simple definition in terms of fundamental physics". Rather, it can't be given any sense at all.

The thing is, Eliezer jumped directly from "physical continuity can't be given sense in terms of persistent identity of fundamental particles" to "we should stop caring about physical continuity" while skipping the step of "physical continuity can't be given any other sense". How did he do this, except by relying implicitly on the assumption that it should "have a simple definition in terms of fundamental physics" or something similar, even as he would surely deny this assumption when considering it explicitly?