We do and straight after departure get a C check to verify. There may have been a problem with height info at low level perhaps?
And it's not OUR airspace, but if a relatively un-manoeuvrable airliner wants to deviate from the myriad of airways available to save time and cash then the captain takes his/her chances in Class G, and should get all snooty when fighters dare to be in his/her way. Or worse, dare to have the danger areas segregated so the original flight plan must be followed. Danger areas where we also wear C.
Rant off, Happy New Year, safe aviating.