I took it as a simplicity issue, or unsophistication, rather. That actually may be the same thing as your control issue. The poem gives me the image of a specific person- not a specific person with a name, but a specific kind of person. (Of course that specific kind doesn't completely exist in reality. The most seemingly simple and transparent person always has something else going on.) Like the kind who would beat his wife if she wouldn't fight back and sell his kids if he found a buyer... (this is what I call a redneck, the rest of you would probably call me a redneck just for the fact that I live in the middle of nowhere Georgia, refuse to spend more than $10 on a shirt, and don't even have a car, so this is the redneck view of a redneck

maybe it's selfishness that I'm getting at, but I think you are right, there is a control thing as opposed to a freer "feeling" thing.
Of course some would see it exactly the opposite I do. Crysanthemums, hemlock, and black tea are all the "cultured" choices, but that equates to controllable, and I had exactly the same reaction to the name line, though not necessarily for the same reason as I saw a preference for money as an indication of simplicity and selfishness.
The part I found the least meaning is is the part about summer and preferring winter with burning chimneys. Huh? I guess if you look at it from the same as the rest, winter keeps people inside where they create their own environment as opposed to the natural one. A lot like, say, a desert made of brown sugar over fruit.
And maybe she chose the title "chainsaw bears" to show the absurdity of people's fixation with controlling their environment as opposed to just using what's there- ridiculous like a bear with a chainsaw?