In addition to the "safety factor", ease of service, keeping any "mess" outside, no necessity for alterations to house, no chimney to maintain, and definitely not least, hot water heat, "transmissable" to several buildings, are also "advantages" of the (Taylor at least) outdoor stoves.
Regarding safety and "indoor woodburners", as a retired firefighter, I can say that the Burn-your-house-to-the-ground (and maybe you with it) potential is nothing to take lightly, nor the damage to interiors of homes and humans from carbon monoxide, soot etc.
True, millions of homes have fireplaces/woodstoves, amd enjoy them safely, but many others somehow do not "get around" to the VERY necessary maintenance, nor apply the most basic safety practices. Throw older(perhaps senile) persons and small children into the mix, and the level of "wariness" required becomes simply more than many can or will really maintain.
I'm biased in my view, of, course, but unless one has experienced, or at least thoughtfully-witnessed the shattering of lives and unexpected sense-of-loss resulting from serious fires, it is difficult to imagine the real effects. Most people find that much more than "just things" are taken from them by fire.
When I build my new home, there will be no "fueled" (gas/oil) appliances in it. Heating will be electric and hot water(from an outside stove - we have plenty of wood!).
There will also be a fireplace, because the pleasures of the fireside are worth something also, and I know I will see to the safe use of it, on the occasions when it is desired... but it will definitely NOT be the "everyday" source of cold-weather heat.
My own suggestion, for those who want to "remodel" by adding a "watchable" and cozy stove/heater, would be one of the newer pellet-stoves, installed and maintained strictly to the highest safety standards.
I expect to be "called-on-the-carpet" by some whose families have coexisted with and enjoyed fireplaces and older woodstoves for generations

.
I believe it, and wish today's "consumer" was as capable, on a common-sense level, as our grandparent's generation. Unfortunately, (and maybe I am just getting old) I don't think they are. I'm speaking generally of course, and know that many exceptions to this are out there...and Tractorbynet is probably a good place to find a bunch of those.
Just one man's thoughts!
Larry