For the last couple years since I moved to my new place I haven't used one but that's just because I haven't got it installed yet.
When I was living in my mobile home in the other town I used my wood burning stove as the sole source of heat.
I never got gas installed to it since the home was only temporary and I used the wood stove in the winter to cook on as well.
If installed correctly they're very safe. I know how to install them safely so I didn't need to pay anyone to install it for me.
But if I didn't know how to correctly install it I would hire it out as they must be installed correctly with the triple wall pipe and proper clearances to anything combustible.
Since mine was installed correctly I had no problem going to bed at night with the fire going in the stove.
Natural gas furnaces can be dangerous too if they leak gas and blow up.
In my old house that was built in 1906 while remodeling and taking down old lathe boards I found places where stove pipe was installed in the living room, dining room, and bedroom.
It's all these old houses were heated with mostly back then.
I love wood heat and it saves money too if you can get the wood for free.
Yes it requires work but I love cutting, splitting and hauling wood and lighting up my wood stove.
I love coming in from a cold day outside and standing next to the stove until my pants start getting so hot they will smolder if I don't move away from it.
To those out there that don't love wood burning stoves and do have a gas heater that requires no electricity as a backup. Remember that just like electricity a natural gas supply can be cut off too.
Always have a backup source of heat.