I fly 737’s to Class G airports, and I’ve never had to wait outside class E waiting for a clearance.
Not saying it can’t happen, but if it did it doesn’t burn much more fuel. If I can’t get a clearance it will be because there is another aircraft in my way. In that situation I’d rather stay out of it’s way!
On the other hand, I’m almost always held down at 5000’ for several minutes departing 34R in Sydney in Class C.