When are they not a good idea?

Been planning on using a rocket mass heater for a long time to heat the home we're building. Bought the books, built a small one in the greenhouse to prove concept and design, watched a crap ton of videos on it. Now my spouse is telling me it isn't a good idea to put one in because our winters are variable in temperature.

What? Sure we don't have a deep freeze from November to April to contend with, but it gets cold. We have to run a heater from October to April most years to keep from freezing pipes and toes and such. It's not like it's 80 degrees outside (although we do have a few of those rare days).

But it got me to wondering is there ever a situation where a rocket mass heater wouldn't be appropriate for heating a home? The tropics, sure. Zone 9 and above, sure. But just because you don't get snow every year doesn't mean it's inappropriate to use one, right? I mean the point is that it delivers an even heat consistently with little fuel, so if it's colder you use more fuel and if it's not so cold you use less ... or did I miss something along the way?

So you can build a heater anywhere on a range from negligibly massive (like a cast iron woodstove) to extremely massive (like Rob Roy's enormous central column masonry heater, 22 tons IIRC).

A negligibly massive stove will heat up very quickly, shed its heat very promptly, and be cool again very quickly.
An extremely massive stove will heat up very slowly, shed its heat very slowly, and not be cool again for quite a while.

The problem I expect your wife is picturing is this. In places with cold winters, there are the "shoulder seasons". That's the transition time between the peak and the trough of your heating demands. And in the should seasons, it's often warm during the day but cool enough at night to want a fire. It's also often cool for a couple of days, then a warm front moves through, and then it's warm for a few days, and then switch back again.

If you have a rather massive stove, you might burn a fire and not feel much heat for four hours. With practice, you can maybe judge this correctly, and light a fire at 4pm so the room doesn't cool off at 8pm. Only if you're home from work, though. And you remember. And if you're coming back from a trip, say, you've got a chilly several hours ahead of you.
And also in a stove that massive, it might NOT cool off as much overnight as you want, so that midmorning is uncomfortably hot the next day.

That's the trade-off involved in mass. It stays warm a long time when you want it to (in the dead of winter).... but it also stays warm a long time when you don't want it to (in the shoulder seasons).

In my view, there's another, very important effect in play. Specificly, the temperature difference between the heater and the surrounding air. When the temperature difference (called delta T) is greatest, radiation will stream out the heater and into the living space at a certain rate. The smaller the delta T, the slower the heat is coming out. Ultimately, when delta T is zero, transmission of heat will stop altogether. In effect, Delta T isn't very large concerning a mass heater as compared to a cast iron box stove to begin with. When fired sparingly in the shoulder season it won't over heat the house since the mass is just a few degrees warmer than the surrounding air, nothing more. A mass heater is acting very, very different in this respect and shouldn't be viewed the same as an iron stove.

In my own situation, the house is never overheated in practise which could happen in theory in a passive house like ours in a mild seaside climate such as the Netherlands. Our heater is 2 metric tons of weight and when the sun comes in we aren't driven out by the heat.