Australia is a pretty good example of such things happening. For instance take the small-ish town of Kununurra in Western Australia, it is serviced by by 2 operators Air North and Skywest and has no Tower service there. It also used to have a significant amount of Charter and Scenic Flights which came and went.
Broome used to be a bit of an odd one as well up until a few years ago when it gained a tower. Previously it had a CAGR (Certified Aviation Ground Radio) which was an Information Service.
In Vanuatu there's an Airport called Santo/Luganville, it services domestic/international and has a Flight Information Service there as well who are fond of the phrase "Runway is Clear" as aircraft make their final approach!!
So I see no reason why they would not continue services into most so long as their "Risk Department" decide that the amount of traffic in and out of the proposed aerodrome poses no more significant risk than in controlled airspace.