Aan airport we most often use as the alternate for our homebase had a notam like that for a while.
The problem was that they were remodelling the terminal including immigration etc.
So they couldn't handle aircraft diverting to that field and expecting to deplane and proces the pax on top of the schelduled flights.
But the airport itself was perfectly able to handle the aircraft landing and responding to it in case of an emergency.
I would be perfectly happy to select that airport as an enroute alternate, since it would probably require an emergency for me to go there anyway.