They could at least get the acronym right... We're not Physical Medicine Rehabilitation. The ampersand is what makes our specialty name (sort of) cool. The French may leave it out, but when you have a French accent you can do these sorts of things and people love it all the more.
Personally, I'm not sure we'll get over-saturated anytime soon. As you point out, we're a small field. On the inpatient side, we still don't have enough physiatrists. Lots of units don't have a permanent rehab doctor, and many don't have a rehab physician at all and are using IM or other specialties. So there's still plenty of room for more on the inpatient side.
Outpatient MSK has always been underutilized. Part of that is we're not well understood, so we don't get the referrals we need--and our small numbers further compound that by making us less common and less likely for providers to know they can refer to us. So I think as ortho groups and neurosurgery groups (and PCPs in general) better understand what we do, we'll get more outpt referrals. Plus, with the way things are going we'll see more PA/NPs, which means more referrals for back pain that will probably cure itself. But at least those patients will love us!
There have never been enough peds PM&R or "general outpt PM&R" (stroke/SCI/amputee care).
I'm not so sure there's much more room for interventional/pain on the other hand.
Just my two cents. I am in SF or LA though. Maybe the big cities are a bit different?