I live in a rural area in the Western US with some acreage, and try to avoid the use of herbicides as much as possible when I'm controlling weeds and invasives on our property.
Flame weeding is far and away the most fun and satisfying way to deal with weeds, but it doesn't seem to do much for me beyond perhaps briefly annoying them.
I've tried both near complete obliteration, and damaging the weed somewhat lightly under the theory that it'll expend its energy trying to "repair" itself, and die out more effectively in the long term.
Neither seems to work well with the thistles and other plants I'm fighting. I've even seen some thistles come back particularly strong after a fire. My theory is that seeds from competing plants are burned, but thistles underground network of rhizomes are unaffected, and take advantage of the lack of competition.
I recognize that fire is a natural and important part of the landscape and ecology of the West, but when it comes to crisping weeds, it seems to have limited use in my experience.