Given the state of many roads (potholed, unsurfaced and crazily steep and winding) I can't see how a large bus could even get around!
In Iceland, buses travel places 2wd cars, even the more basic 4wds, can't go. I don't recall many crazily steep and winding roads in Iceland.
The problem with service buses is that they mainly go to places people live, not tourist attractions, though there are additionally, and importantly, seasonal excusion buses that serve the main tourist attractions. With only one bus a day in many places, and less than that in some others, you can't just hop off, have a look and wait for the next one, as that might be tomorrow, or worse.
For many purposes, such as certain of the main non-circular walking routes, a bus can be a more convenient form of transport than a car.
if you want to get off the ring road, the only option is hiring a car
It is obvious from the bus timetable links shown that buses do a lot more than the ring road: they go to main settlements and tourist attractinos, and around the Westfjords and Snafellsness, and right across the interior by several routes, etc. If you want to get seriously off the beaten track, you might need more than just a 2wd car.
So in sum, buses are inflexible and time-consuming. But you can't go everywhere in a car if it is only a basic one.