Masonry heaters and catalytic converters/secondary burn chambers are somewhat unrelated. The masonry heater forces the exhaust gas to keep as much of its heat i

Masonry heaters and catalytic converters/secondary burn chambers are somewhat unrelated. The masonry heater forces the exhaust gas to keep as much of its heat inside the indoors as possible. An efficient stove produces a very efficient reaction to burn its input fuel, creating higher temperatures and cleaner exhaust gasses. The masonry heater is a solution meant for a time when folks didn't know how to cleanly/hotly burn wood. The two methods (efficient wood stove and masonry heating) can be combined for even more heating efficiency. The problem with masonry heaters is that they require the house to be built alongside the masonry heater (e.g. you need to run the thermal mass inside the house so it can convect heat into the house). The thermal mass required can also be very expensive and/or labor intensive to make. Moreover cleaning a masonry heater and maintaining it can be a large pain depending on the size of the thermal mass. Catalytic converters have been in widespread use for automobiles since the '70s (that's ~50 years) so they're pretty proven technology now. Secondary burn chambers are even older (early 1900s I believe.)