The dive profiles and procedures are usually mandated by the skipper, in some areas by law, and should always be mandated by common sense. There are recreational dive charters and there are technical dive charters. Either can be done OC/RB exclusive, or mixed. Some skippers allow solo dives, others don't. Has nothing to do with RB divers.
If the boat you're on is a recreational boat, filled with recreational divers, no one wants to wait for either an OC or RB diver to return from a three hour deco dive.
As far as accidents are concerned, there is no major difference between the diver being on OC or CC. Either he has an accident or not. Either the crew is well trained and has an accident protocol in place or not. If you're diving a wall or pinnacle on OC, run out of gas and sink or if you plan to go past 130 ft and have a problem there, either way you'll be within reach or not. Most likely we're talking recovery anyway, as surface support usually happens at the surface.
With the exception of caustic cocktails, everything that can happen on a rebreather can happen on OC. Maybe with a lesser chance, but it can happen. And chemical burns to the mouth and throat certainly can happen with all kinds of chemical substances found in every household and on any boat.
Relying on the Coast Guard to save the day is foolish, threads in the accident forum already discussed this. They may already have an incident or accident to deal with, same with hyperbaric chambers. You may just be out of luck.
It is up to the local dive operator to know what if any third party support is or can be available, and have contingency plans in place. A well trained crew providing first aid to an injured diver can go a very long way saving his life and health. An EMT or MD on board increases chances, as does DAN support. But diving has its dangers, and in some cases the best team, the best support, the best doctor and fastest Coast Guard chopper won't be able to make a difference.
If anything, CCR divers have an additional O2 supply they can stretch for several hours if they have enough sorb and the rig's still operable. That's what DAN's REMO unit is, a small surface rebreather for Remote Emergency Medical Oxygen supply. Also, the CCR diver may well be able to be on 100% O2 while still submerged 18 or 20 feet, all the way to and at the surface while waiting for support from the boat.