I have a Rotator SWB that I bought used. It has a mid drive, with a 5 speed mid and 7 speed rear cluster (mid is fixed, rear is a freewheel). It uses twist shifters, the front has a 7 speed but only uses 5 of them.
I think it is great. The mid shifts much better than the front on a traditional setup, and you can shift either one depending on where you are on the respective clusters, until you get to the highest or lowest gears.
I can see why this would not work on a DF, but wonder why it is not more popular on recumbents.

It's usually overkill. I have some Sunset lowracers with it, and while nice, it does add a complication.

The difference isn't huge, but if you do the math, small drive wheels mean less total gear range. If the range becomes an issue, the answer is to take 'extreme measures.' That can mean a Capreo 9T gear in back, or adding internal gearing at the hub or the bottom bracket, or in the case of Rotator a mid-drive with more gears.

I had a mid-drive on my Greenway trike and found it surprisingly quiet.

I like the mid drive on my Dragonflyer as it makes up for having 20 inch wheels all around. It's quiet, is at the midpoint of the trike allowing for have the pivot point for the shock in the middle of the trike. Seems to have enough gears as I can get up most hills in my area without stopping. 3 in the front and 8 in the rear.The trike has a few years on it but was a bit ahead of the rest at that time.

Actually the Rotator mid drive cassette is mounted on a pair of sealed bearings with an ID of 10mm. The shaft is a 10mm axle cantilevered off the main
tube and held by a small tube welded at a 90D angle to the main tube with an internal 10Mx1.0 thread. The cassette splined carrier is standard Shimano
splines and the sealed bearings are at either end of the splined carrier. Inboard of the mid-drive cassette is the drive cog for the rear wheel cassette.
All of these cogs can be obtained by looking for cassettes held together with screws and not using carriers for the larger cogs. These used to be available
for $5-10 from Nashbar but have gone up the past few years. The better known Shimano/Sram cassettes all use carriers for the larger cogs and are not
suitable cog donors. You need to rummage for off brand 7-8-9 speed cassettes without large cog carriers. Rotator used standard 10Mx1.0 solid axles for
their mid-drives and had to shim the middle of these with a wraparound shim glued to the shaft for them to fit well into the bearings. It only takes a few
degrees of skew in the axle to allow the rear chain to derail under torque.
The axles had an actual diameter closer to 9.5mm where the bearing fit and 9.8mm at the threads, at least on my axle. The skew angle problem necessitated
manufacture of a new axle at home. First attempt with carbon steel solved the skew angle problem but broke after 800 miles. Second axle out of 4140 lasted
5500miles, and the 3d axle also 4140 is still on the bike after 13,000 miles. I lengthened the axle so I could put a nut on the L side of the mounting tube to snug
up the axle and made wrench flats on it for easier removal 'if it breaks'. The axle is under
a lot more torque than you would think, as both breaks occurred with strong accelerations, fortunately not too far from home.

The Sunset looks more like an idler set up than a Rotator/Trek style middrive.

It's a fixed ratio mid drive to step up the gearing to mimic a 700c drive wheel.
Usually 1 : 1.5 , but the cogs are replaceable so it could be whatever you want.

If I had thought about it that should have been obvious. delXV reminds me of my days as a physics/math undergrad..... Long time ago. Vector analysis, one of
my more fun courses.

I guess I have been lucky, nothing has broken and I have never dropped the chain. The cogs in the mid drive look to be thick steel, I can't imagine wearing them out, nor being strong enough to break the axle. Having said that, I bought it used and cheap, so if I did break something I'm not sure how much I would put into it (and I am not a machinist, so making parts is not a realistic option.) I did go through it and redo all the bearings, clean and adjust the derailleurs, true the wheels, etc.

I'm not sure just what all goes on there. The description reminds me of the drivetrain on da Vinci tandems. The claimed advantage of the system is captain and stoker can coast while the other is pedaling. However, one consequence is that the "front" is a half-size set of chainrings with 4 cogs on it instead of the normal two. So it's a fourple instead of a triple.
Drivetrain Info - da Vinci Designs

You could certainly use the Da Vinci components to create a recumbent mid-drive.

To address Mike W's original question: "[I] wonder why it is not more popular on recumbents."

Recumbents are already a small niche market product, requiring a custom frame, seat, and some accessories. To add custom drivetrain components simply adds cost and difficulty to an already costly and difficult-to-manufacture product. In short, mid-drives aren't more popular because the benefits aren't worth the costs.

FWIW: the Aerocoupe trikes I built used a modified tandem crankset to create a sort-of mid-drive arangement. Modifying the crankset was a significant investment in time and tooling.

Best view: (from river12 )

Reminds me of the birdcage Masarati sports cars of the 60's. The space frame chassis was fabricated from multiple pencil diameter tubes. The joke was they removed one tube at a time until it broke then added the last tube back.

Thanks. It was a beast to fabricate, though, with all those small tubes.

My 1st trike I think was called a Rotator Comfort3. With the mid drive(6) and rear Derailluer(8)and the crank had a single gear(34T), it was a great tour machine. I rode the Icefield Parkway Alt., Vancouver Island, Gulf islands and the Sunshine Coast with that beast. Now I'm riding my 2nd Catrike 8yrs later but still recall those days, especially getting used to riding with all kinds of traffic, I thought I was low to the ground then....

That is very similar to what I have, although I have 5 and 7 rather than 6 and 8. I srikes me that the mid derailleur is a lot more vulnerable on a trike than a 2 wheeler though!
I think the biggest advantage is that all shifting is done with "rear" derailleurs that move the unloaded side of the chain, and therefore shift more quickly and reliably than any (mechanical) front derailleur I have ever used. There are so many combinations with so much overlap that I just shift whichever will keep both as close to the center as possible.