But that wouldn’t necessarily obviate Christian universalism, which (at bottom) isn’t primarily about what sinners do or don’t do, but about what God does. As long as God is continuing to act toward saving everyone from sin, universal salvation is still technically true, even if it happens that some sinners never repent.
Which is why practically every Arminian I’ve ever read or heard (including my teacher Lewis) go out of their way to try to explain that God eventually gives up on sinners (so in fact becomes angry forever, completely regardless of whether the sinners are unrepentant forever); or else is defeated in His attempts (by those sinners or by other sinners in regard to those sinners, e.g. Satan permanently wins some sinners into hell despite God).
The concept that the door to hell shuts from the inside, at any rate, is very far from a Biblical one. No Arminian who comes up with that (even my teacher Lewis) has any excuse afterward to complain that Christian universalists preach unbiblical doctrines! The uniform Biblical testimony (so far as I recall) involves God directly punishing sinners, or God saving sinners after their destruction by God leads to repentance. The Son descends into hades to preach (so it’s hardly locked from the inside, regardless of what that testimony is supposed to mean); the gates of hades will not stand strong against the church of Christ; and as RHM pointed out Christ has the keys to death and hades.
I can recall some brief testimony to the effect that sinners in the grave aren’t happy to be there (welcomed by maggots etc.), which is very far from being the same thing as locking the doors to the grave from the inside; and I can recall some testimony to the effect that sinners wailing and gnashing their teeth outside, but each of those situations involves them being thrown outside by YHWH/Christ, so it isn’t a case of them locking the doors from the inside.
That concept tends not to fit well with supernaturalistic theism, either, in terms of coherent metaphysics. If sinners (or anything else) start to exist independently of God (whether self-existently so or in ultimate dependence on something else), then a metaphysic other than supernaturalistic theism is being proposed to be true. Anything that stays in existence, God actively keeps in existence; which involves omniscience, and omnipresence, and omnipotence.
That isn’t a problem for annihilationists of course (Arm or Calv either one); but it would be wildly contradictory to say that the reason God can’t save sinners He annihilates is because they refuse to repent and insist on locking the doors to hell from the inside. That’s an ECT defense, not an anni defense.
(An anni could try claiming that people annihilate themselves by locking the door to hell from the inside, but that isn’t quite the same thing. It also leaves aside the question of God’s authoritative intentions–they could only do such a thing by God’s direct permission, so in fact it is still God Who is choosing to withdraw His action to keep them in existence. Or else the anni proponent is denying supernaturalistic theism by claiming that people can annihilate themselves regardless of the action of God to keep them in existence.)