If you're coasting down a hill to a stop, then it's better to coast in gear to use approximately no fuel. If you're coasting down a hill to long level stretch of road it's better to coast in neutral to obtain kinetic energy. If one wants to follow speed limits it's sometimes necessary to first coast in neutral then use engine braking at the bottom of the hill.
The optimal strategy in all cases is actually coasting in neutral with the engine turned off, and then starting the engine when you need to increase your speed. (This advanced technique may be illegal, though).
Apparently Mercedes call it "glide mode" or "gliding mode" depending which bit of marketing you look at. I couldn't find a technical description though (beyond what you already said).
Understandably it is dangerous as you are not in control of the transmission and therefore the wheels, hence the failure in the UK. But I got through some incredibly scarce times by coasting a bit on the commute to work...
With automatics you would need to brake down the hill to stop the car "running away" as it wouldn't engine brake automatically to compensate for gravity's effect.
Most automatic transmissions (or at least the ones I've driven, which arguably is not more recent than late 90s) have low ranges where there is engine braking. That's the exact use case for them. Automatic doesn't (or didn't) mean that you must never shift manually.
Automatic transmissions in large vehicles like trucks and buses usually don't have freewheels either, so there is always engine braking.
Right, but when you're coasting you're burning fuel to turn over, unless you have a perpetual motion engine. Whereas engine braking (on a car with an ECU i.e. one made since 1996 or so) you could be doing 2000rpm but burning no fuel (gravity is turning the wheels which are turning the engine).
... which brakes the car, so you still lose energy.
Can't find literature at the moment, but ISTR that the valve train can take several kW to operate.
Well, of course a hybrid has engine braking - that's kind of pivotal to the whole hybrid design. It freaked my wife out the first time we went down a 7% grade in ours in 'B(raking)' - once the battery charged holding down the brake pedal caused the second MG to disengage from the transaxle and spin at max RPM's to bleed off the excess energy.
But yes, every automatic car I've ever been in has had engine braking as well - going down the same grade by mother will shift her Chevy Impala into '3' and can easily coast down the same hill only applying the brake to turn corners.
Would be nice if our Prius didn't require holding down the brake pedal, but in a way I think it plays into the natural instincts of a driver to do so - but it's a habit that can get you killed driving a manual or standard automatic transmission by overheating the brakes, so hopefully my wife doesn't go down any grades in a car other than our own without me.
Every generation of car is getting better at all these things, so statements about efficiency almost all need a "cars built prior to 20XX".
In the UK you will fail your driving test if you coast, and in some countries / states it is illegal - with good reason.
Just google it - not a single article supporting your argument.