The Royal National Lifeboat Institution’s “class D lifeboats” are an example of the kind of inflatable boats the U.S. Coast Guard could operate from its larger response boats to reach remote shallow waters, shoals, and beaches. (RNLI)
The US Naval Institute Proceedings has a short article addressing a perceived gap in our SAR capability. His suggested solution is a smaller boat capable of operating in very shallow water, carried by our Response Boats.
Even if it is not possible to carry the smaller lifeboat aboard the Response Boat, it might be possible tow one astern, if it is clear that the case is in shallow water.
We might also be able to develop something using a line throwing gun and a float or special lifejacket.
In any case, this is excellent feedback from operator and probably deserves some consideration.
Chuck Hill's CG Blog 
When I was at Station Mare Island, we would tow a small Boston Whaler behind the 32′ to gain access to some of the sloughs and shallow areas of the Sacramento River Delta.
I’ve seen the Canadian 47’s carry a small inflatable with a modest outboard in British Columbia. There’s no reason that this can’t be a standardized capability in the USCG rather than various stations reinventing the wheel to solve a common problem. Hell, I think I saw a Cape D boat crew take a MWR canoe on a televised rescue recently.
Something like that would be perfect for the Coast Guard Auxiliary side as well and I can see every flotilla, division and district would have a small inflatable for near shore SAR or River SAR
The RBM’s have a large open space on the stern that should accommodate the RNLI boat pictured above, might be a stumbling hazard however. If deploy in 3 minutes was not required storing an inflatable deflated with a small air tank for quick inflation might also work.
A hundred years ago they had line throwing cannon (Lyle Gun) and I have seen line throwing rifles from time to time, with advances in electronics today they should be able to make an accurate line throwing rocket of some sort that would be easy and safe to handle, being able to stand off a vessel in distress could be an advantage in adverse conditions.
How about some of these….
Simple and comparatively cheap..
More expensive…
Or team up with the RN who are doing a lot of work on UAV’s for man overboard situations. The eventual idea is the UAV is launched quickly, can find the man overboard autonomously, drop life saving gear and hover over the casualty so that the vessel can locate them for a rescue.
https://www.royalnavy.mod.uk/news-and-latest-activity/news/2021/july/02/210702-drone-trials-mob
A little bit more expensive but a lot of uses…
The larger Malloy T-650 that BAE are working on will carry a Stingray torpedo, which way 270 kg (almost 600lb). That means it could carry a rescue strop and a casualty out of the water…
https://www.janes.com/defence-news/news-detail/dsei-2021-bae-systems-and-malloy-aeronautics-unveil-t-650-all-electric-uas
That would help also – I think I have seen these types proposed for shore base lifesaving stations – can be sent out quickly from the shore. They could also be used to send a messenger line for a tow line
Parts of Lake St. Clair are really shallow. A boat on plane that stops will often settle into the mud and get stuck. Someone in D9 wanted the local 41 to carry an inflatable to rescue people that got stuck. I told them that if the boat was in less than 3 feet of water the people should just get out and walk…
Sea Eagle sells a 14 foot inflatable orange rescue boat that can handle a forty horsepower outboard motor with a hard plastic floor or twenty-five horsepower motor with an inflatable floor. The weight without motor is less than two hundred pounds for both, and the boat has a capacity of seven adults or 2,000 pounds. The base price is somewhere around $3,000 without motor, and it can be inflated quickly with an electric pump. I have two Sea Eagle inflatables, one of which I have used in whitewater and bounced off a number of rocks. They are good boats..