That's not my experience.
I ran a simple negative-ion generator in my office for several years, when I worked in Los Angeles in a building right under the LAX approach path. Lots of soot, jet-engine exhaust fumes, etc. in the air... really yucky.
The negative-ion generator had a very beneficial effect on the air in the office. I noticed no increase in ozone (there was quite a bit in LA air at times in the summer, and my eyes are quite sensitive to it). I presume that the discharge voltage was kept low enough to minimize ozone production.
The "deposits soot and dust on the walls and furniture" problem was quite real. The gunk precipitated out of the air didn't get back in... rather, it ended up plating the ceiling tiles, the painted walls, papers and pictures tacked up on the walls, and so forth. After 2-3 months of operation I could see a "shadow" on the wall if I removed a photo or calendar. The gunk would not brush off of the wall... it was there for good. When I left the company, I understand that they decided to repaint the whole room... the gunk wouldn't wash off.
I definitely had less allergy symptoms when using the generator... and the most subjectively pleasant and breathable air in the whole building.
On the other hand, I've been in rooms where an "ozone purifier" was being operated. Nasty, nasty, nasty... my eyes were burning after only a few minutes. I'd never buy one of those things.