Declaring an interest: we're Build4less, a building materials supplier.

I think you've named the biggest obstacle yourself. A well insulated, airtight new build might only need a couple of kW on the coldest day and far less in spring and autumn, so a heater sized to store a full firing tends to overheat the room it sits in. In older solid wall houses with a higher heat demand they make a lot more sense.

The other obstacles I'd expect are these. Weight: a tonne or more of masonry needs a proper foundation, and most UK houses have suspended timber ground floors, so a retrofit often means digging out for a pad. Smoke control areas: much of urban England is covered, and a site built heater isn't going to be on the Defra exempt appliance list, which rules out burning wood in it there. Building regs: Part J still applies to the hearth, flue and air supply, and with no installer self certification route for a bespoke build it has to go through building control, which puts people off. Air supply: in an airtight house it really wants a ducted outside air feed to the firebox. Then there's simply space and cost against a conventional stove or a heat pump.

I'd say the best fit is rural self builds on a ground bearing slab, with the heater in the middle of an open plan layout, plus older solid wall homes. A modular refractory core with a local mason doing the cladding might help bring the cost down.

We had several masonry stoves but now only 2 left (in separate houses). They tend to be big, weigh a ton (literally) and usually dominate the room in which they are located. Over here (Hungary) they were very common 30 - 40 years ago but not so much now. An external air supply is difficult to arrange and like any wood burner in a room they tend to created dirt and dust around them.

Contrary to the comment of build4less I think that in a well insulated house a masonry stove would serve better than a modern wood burner as the heat is stored and released over time. When we light the one in our lounge in the evening it is a couple of hours before heat is emitted but it is still warm the following morning, whereas the modern 5kW stove in my sisters lounge made the room uncomfortably hot within an hour and was cold about 3 hours later.

IMO they are only suitable for an owner / occupier who is prepared to manage the use of the stove as they need to be run properly and miss-managed can build up combustion gasses that can blow the top off the stoves when they ignite. Also burning wood that is not properly seasoned would be the death of one as the tar build up would destroy the internals. Even properly managed they will need periodic re-stacking which involves the same labour cost as building new.

Wood burning is going out of fashion today and with the regs in the UK I would be surprised if you could get regs approval for a bespoke stove without considerable expense in time and cost.

Having said all that, tests done some years ago showed that a properly designed and build masonry stove can get efficiencies of close to 90%.

Ours has done us well but is close to needing a re-stack and when its time is due we will be removing it and replacing it with a modern wood burning stove with external air feed.