According to an old Straight Dope column, some air fresheners use nasal anesthetic. In other words it works by numbing your nose, not eliminating the bad smells.
As mentioned they may have contents that reduce the ability to smell odors, or maybe sometimes to encapsulate the particles we smell (not sure that describes what happens). I assume they emit fragrances that will hide unwanted odors for others. I assume they don’t oxygen generators or the like to actual neutralize odor particulates in the air. I think those are the only means air fresheners use that aren’t moving the air in or out of a room.
In that case you could return them and get your money back. Products sold must be capable of performing their intended function. Of course if they just emit some kind of additional masking odor you have no case. It’s much easier not to buy them in the first place.
It’s possible that your sense of smell isn’t as sensitive as your wife’s. If so, that would mean both that you don’t detect the subtle aromas they provide, and also that you don’t detect the subtle unpleasant odors that they cover up.
My experience is those things usually stink. Both Mrs Fluffy and myself are pretty sensitive to fragrances and nothing scented comes into our home. I hate those things, but they definitely emit a odor to me.
A spray air freshener is going to be more effective in a bathroom as you dose the room when it is needed after an event, rather than relying on some continuous release.
If there is no window or fan I still prefer to light a match it seems to work very well and doesn’t smell like a chemical flower.
My experience is that they simply add another odor to the room.
We have a pine-scented deodorizer in the storage room at the library where I volunteer, and it’s a pleasant natural odor. Our director brought one in a while back that she said was the floral scent she used at home, and it was giving everyone else headaches and even permeated my sinus cavities, so she took it back home. I’ve never been to her house.
I HATE those things, they smell terrible. I prefer decent ventilation to freshen the air in a bathroom.
But if your wife likes them, and you don’t notice any effect at all, and they are cheap, the obvious right answer is to use them. Neither the cost nor the effect bothers you, and she likes them. So using them is a clear win.
Also the story with Febreze as the first odor eliminator was that no smell did not sell. People with cat smell houses that made others gag acclimated to it and did not smell it themselves. The perfume was required to convince them it was doing something.