Do you think the byproducts that result from the reaction with ozone are safer to breathe? If not, then you need to air out the room or filter the air, so why not just do that in the first place?
Just because you can't smell something because it has been "destroyed" by being converted to something else doesn't mean it's not harmful to health.
Again from the EPA:
https://www.epa.gov/indoor-air-quality-iaq/ozone-generators-...
"First, a review of scientific research shows that, for many of the chemicals commonly found in indoor environments, the reaction process with ozone may take months or years (Boeniger, 1995). For all practical purposes, ozone does not react at all with such chemicals. And contrary to specific claims by some vendors, ozone generators are not effective in removing carbon monoxide (Salls, 1927; Shaughnessy et al., 1994) or formaldehyde (Esswein and Boeniger, 1994)."
"Second, for many of the chemicals with which ozone does readily react, the reaction can form a variety of harmful or irritating by-products (Weschler et al., 1992a, 1992b, 1996; Zhang and Lioy, 1994). For example, in a laboratory experiment that mixed ozone with chemicals from new carpet, ozone reduced many of these chemicals, including those which can produce new carpet odor. However, in the process, the reaction produced a variety of aldehydes, and the total concentration of organic chemicals in the air increased rather than decreased after the introduction of ozone"
"Third, ozone does not remove particles (e.g., dust and pollen) from the air, including the particles that cause most allergies. "