Class H amps?

Can an analog Class H still have (would make sense) a switched mode power supply (LOTS of weight saving right there)? 

Absolutely.  This seems to be what the NAD Hybrid amps are doing, but they have very very little information out in the public domain.

Yamaha's EEEngine amps also have this type of design. 

One engineering difficulty about Class H though is the voltage rails have to anticipate the signal peaks.  There's some interesting discussions online about Yamaha's implementation, distortion, and fixes.  Class G solves this problem by having multiple rails available all the time, but this adds to the possibility of distortion when those rails switch.

So if Class H is still analog, what is BENEFIT over A/B. Just power consumption/weight?

Yep, attempt to get to Class D efficiencies of manufacturing as well as power usage without the switching issues.

If the linear amp is kept in Class-A, then the efficiencies over a Class A are really outstanding. AFAIK, they make no claim that H is better sounding than A or A/B, but as good, with much higher efficiences.

The point made elsewhere, that it’s all in the implementation, is really important.

It may help to understand that due to FTC rules, most amplifiers have to be heavily overbuilt.  FTC rules require pre-heating at (I think) 30% of the rated power for an hour before testing for noise, distortion and output.  This is a situation never encountered in music.  If you have a 300 W amplifier, you don't play music at 100W continuously.  To meet the FTC requirements an amp must have excessively over-built heat sinks, which adds so much to manufacturing and transportation costs.  Anything that reduces the weight of an amplifier not only makes it cheaper to make, but greatly reduces the carbon footprint. 

The output transformers are valves between 2 voltage rails. Say, + and - 10 V.

In A, B and A/B those rails are fixed values. Classes G and H vary those rail voltages. Carver and NAD got famous on G. The idea is that minimizing the difference between the rails and raising them only when needed minimizes heat of the output transistors.

NAD continues to dabble with their hybrid Class D amps today.

Wikipedia is your friend: