Fuel hopping isn't an issue - thats what we have tankers for, and Souda Bay isnt that far away to go and top up the tanker. We can also use other NATO assets to refuel.
Furthermore, while I have no doubt that we could get a couple of Helos in to Beirut quickly, it will almost certainly take more than 3 days to get the spares, kit, personnel and everything else needed to support them into place - unless of course Akrotiri is kitted out to support a large SHF op at no notice? The CVS will turn up with all its kit ready to go on the spot, so we have the choice between essentially an almost immediate show of force, backed up by a long wait to get all the kit in place, or 72hrs delay but with everything you want, and unconstrained by being based on land in a warzone.