Not particularly! There are ethicists who believe all sorts of silly things, if you think "self-defeating" or "undermining" qualifies as "silly." For example, there are plenty of ethicists who think that moral statements are really just preference statements, putting "killing is bad" on the same epistemic level as "I don't like peanuts on my sundaes."

This all works out because it isn't actually contrary to their self-interest: academic philosophy doesn't care whether your position undermines some grounding claim, because there's no universal consensus around that grounding claim to begin with. You'll find plenty of moral philosophers who think that morality is a purely preferential mental phenomenon; they don't mind admitting that because there's still plenty of interesting work to be done if that's the case.