Sequential consistency is basically the most lax model you can get away with in this case (and have it generalize to other similar operations). This is a very strong consistency model and weakening linearizability to this basically provides no advantage for availability. There is a proof that anything stronger than causal consistency cannot provide "total availability", which I'd argue is somewhat mythical anyways (except when you're colocated with where data is being stored).
My point here is that this is clearly a case where many of the strongest ordering guarantees are required to get the desired behavior, and subsequently availability must be sacrificed.