Speaking as co-captain of the Albany-Schoharie Cave Rescue team, we're close to the YOSAR model as you describe it.
We don't have formal meetings or trainings. We have a call-out list and a general idea of who we'd call for what sort of rescues, etc.
Sometimes the local sheriff's department (who has legal authority in the event of most rescues around here) will do a quick 4 hour sort of drill early in the year.
We typically manage maybe 1 call-out a year.
So, fairly informal.
Locally (within 1 hour or so of most caves) we have I believe 2 cavers who have gone through Level 3 (and probably 2-3 other cavers who have similar experience from other areas), 4-5 who have gone through Level 2, and depending on the school year, etc. up to a 1/2 dozen who have done Level 1.
We probably have a couple dozen who have done an OCR within the last 5 years.
If we expand the numbers to 2-3 hours, most of those numbers would double or more.
We do have access to a local equipment cache as well as a plethora of personal and other gear. (Yes, I'm a knurd, I keep a sked and OSS in my car normally
With the RPI Outing Club and local cavers, we have plenty of vertical equipment.
Rescue squads and fire departments have pitched in in the past.
(and remember, if you do get called out or need help, contact your local NCRC Regional Coordinator. While the NCRC is NOT a rescue organization, regional coordinators are generally familiar with local resources and can help you gain access to them.)