I doubt the US would send much a presence there anyways. Too much risk of escapism for not much gain.
An Aegis cruiser would be an easier way to provide AD cover for the various drone & ISR orbits in the area than providing 24/7 tanker and fighter cover - and less of an obvious provocation.
As a reminder, the RAF started providing fighter cover for their Rivet Joint flights in the area after a Russian fighter launched an AAM in their direction last October.
https://ukdefencejournal.org.uk/brit...ussian-forces/