I think a warré is a better shape for the bees than the KTBH.
Bees seem to prefer working up or down rather than horizontally, thus the great attraction of chimneys.

That post hoc explanation about bees living naturally in hollow logs; it would be interesting to hear from everyone who has ever come across a colony in the UK living in a fallen horizontal log.

According to Seeley, bees prefer to choose a natural nest site about 15 to 20 feet off the ground.
Did I just allude to chimneys again!

The lack of honey is possibly more to do with management style as opposed to hive shape.
ie, a colony which swarms several times will be unlikely to produce honey, and leaving the bees to swarm seems to go with the TBH warre philosopy for a lot of beekeepers.
A colony riddled with mites, if it survives at all, will not be producing a honey surplus.
Again, lack of effective treatment for varroa is a management issue rather than a fault of the hive itself.

It is quite clear from reading biobees that it is a real struggle for many just to keep the bees alive in a TBH due to the baggage associated with management.
Honey is pretty much a sideshow in this sense as the colony rarely gets to the strength where it can store much of a surplus.

The US top bar beekeepers are probably the ones to listen to as they seem to run them like beehives without as much of an anti everything else agenda.

They probably work a lot better in Devon than they do in Scotland and better still in Kenya.

Be interesting to hear from madasafish why his produce little honey as I think he looks after his TBHs in a sensible fashion.