I just knew this would be an interesting thread right from the title: Suburban folk move to rural area, then complain about rural life. It reminds me of situations here where:
* people complain about farm "smells"
* people complain about chickens (well, specifically roosters)
* people complain about the sound of gunfire in the distance
Even on the home front, the (ex) complained about new houses being proposed down the road (while living in a house that had just been recently built).
OTOH, wood stove operating properly and using seasoned wood should not be putting out smoke all day. I burn between 4-5 full chords of wood per year. I just looked outside and there is no, zero visible smoke coming out. Only when I first start up the stove or for a couple minutes after adding wood.
If your neighbor is splitting up big chunks of wood and then taking them in the house, there is an excellent chance that the wood isn't seasoned properly. In my case, I am using wood cut, split, and stacked early in 2019 and some earlier (2017, 2018). I'm cutting down trees, bucking it up, splitting and stacking wood for the 2021 winter...and even with that I am behind (should have had it done spring of 2020). Fortunately some of what I've been processing is "standing dead" trees (I own 40+ acres of mostly hardwood forest) so I think it can be ready for the next winter.
Someone also mentioned damping the fire down. This could also be an issue (and can be dangerous due to creosote build up). Combine that with green/high moisture content wood and its a bad situation. Not efficient to burn, lots of smoke, can eventually lead to a chimney fire.
Finally, I think the OP is on to something in terms of how much work to keep up a large house. My next move is smaller, and likely to not have any of the toys I've accumulated (lots of land, tractor, trailer, wood stove, steep roof, ...) I can only hope I get someone from the city who wants country life.