Your statement is rather broad and nonspecific. For the most part, all service members have access to the best of dental care. Exams and restorative dentistry is a solid part of the medical care of all US service members at the home base level. If there is any breakdown in the system, this is the first I've ever heard of it.
You get at least one dental exam a year; at that time, at least in the Navy and Marines, your general state of dentition is classified and given a number, 1, 2, or 3. That number determines your deployability based on your dental health. Some conditions, you simply cannot be deployed until the choppers get fixed. Class 2, you can be deployed but certain pathology is noted (carries, still have wisdom teeth, etc).
Corpsmen can do dental care, including pulling teeth, up to a point; then, it gets kicked to a dentist if available. Those class 2 pathologies can worsen in the field, and you can get oral trauma of course, but generally if you get to the field with decent teeth, you will leave with decent teeth unless something happens.
Edited to add, if a dentist isn't available, then as @Teufel suggested the solution may be...innovative.
I am familiar with the Medical Readiness system. According to peer review articles in "Military Medicine" written by dentists regular dental checks (if performed) can only reduce dental emergencies by 40% as trauma and defective fillings cannot always be identified. It has also been said that 75% of dental emergencies during deployment are not preventable. Of course we should not forget the increased consumption of energy drinks which are acidic and cause massive damage to teeth.