are air purifiers worth buying?

The short answer - YES. Air purifiers are 100% worth buying as long as you're getting an air purifier that is effective. My favorite air filters are Austin Air Purifiers https://austinair.com/shop/
These are clinically proven medical-grade air purifiers. These air purifiers were used in lower Manhattan in 2001 and in New Orleans after Katrina and we are using them in our own homes now. Their true Medical Grade HEPA filter removes 99.97% of all particles larger than 0.3 microns and 95% of all particles larger than 0.1 microns - this means a very significant reduction in indoor dust, mold, pollen, chemicals, and gasses that are blunting your body's immune system capacity.

You can read more about what they do and their effectiveness on their website.
Hope this helps!

You ask if an air purifier is better for your health. An air purifier removes particulates from the air which is generally a good thing.

Where I live now, the air is very good most of the time. So I use the air purifier when there are allergens in the air such as pollens and molds. Since I'm not inhaling the allergens all night, it has helped a lot to prevent night time stuffiness and asthma. Going low-carb almost eliminated these problems, but when there is a lot of pollen in the air, I like to make it so my body does not have to work so hard to stay healthy.

I'm in California, so the air purifier has also been really good for removing particulates from the smoke. Since I couldn't really put a face mask on my cats to keep them from inhaling smoke, the air purifier has been a great thing to have for them as well.

I'm a fan of air purifiers especially those that not only filter but emit ozone and ionize the air. Most of these have ozone plates and a UV light as well...typically run $150-200 on Amazon. Also consider adding a humidification system to your furnace for use in the winter months. I like the Aprilaire systems for this that attach directly to your furnace vent.