So many public restrooms use some automated febreeze sprayer to deal with the feces particulate odor in the room. If they used actual HEPA they could actually cut down on the particulate and odors without having the bathroom smell like you are inside a scented candle, or an Abercrombie store. Ongoing costs would probably be similar, HEPA filters are cheap just like a can of febreeze.
HEPA filters do not remove odors. Bad smell is caused by extremely small particles that cannot be removed by HEPA filters. To remove odor, you will need other filters, such as an activated carbon filter. Some air purifiers come with both a HEPA filter and a filter to remove odors.
Classrooms where already an issue before Covid. Concentration goes way down when the air starts to get thick and same goes for meeting rooms. How many times have you entered a meeting room where the air was so thick you felt it as soon as you stepped in?
I'm skeptical that would be good for overall long term health. There are only a limited number of endemic respiratory viruses. Most of us will be exposed to them at multiple times in our lives regardless of what protective steps we take. So I'd rather get them while I'm still relatively young and healthy because the resulting immunity will give me at least partial protection later in life.
Of course ideally it would be better to have effective sterilizing vaccines for all those various respiratory viruses, and perhaps someday we will. But those generally don't exist today for the vast majority of viruses.
There are significant health benefits to cleaner air, not just from infectious disease, but also from particulate pollution and various other harmful substances. I strongly suspect that on the balance it would be a significant net positive from that aspect alone, though I don’t have possession of any hard evidence to back that up.
Elevators, gyms, restaurants.
Not saying it has to happen all at once, but it would help decrease most respiratory diseases from spreading.