I don't use my fireplace, so soot isn't an issue. Also, I'm on the coast in California, high winds for us are <50mph. Also, you've got to be smart enough to not try and overload anything. I've got a single discone on there and it's been up (with a few different antennas) for 12 years. I don't know what they make chimneys out of in other parts of the country, but ours are stout enough that a strong wind blowing on a 1 1/4 mast with a small antenna on it doesn't present enough wind loading to be an issue. After all, this is earthquake country. If the chimneys were so weak they couldn't support a small antenna, a small earthquake would have taken out my chimney many years ago. My home survived a 7.1 quake back in 89 without an issues. I'm not concerned about my antenna install.
The chimney strap mounts don't move around if they are installed correctly.
Finding what works for you depends on your budget, abilities and what you will tolerate. Chimney mounts are cheap and easy and will work fine for low wind load antennas. Of course the actual construction and condition of your chimney is going to dictate.
Other option would be the "Ventenna" if you want low profile and easy install.