You are correct - I hadn't thought of that - but there are so many compact purifiers out there for reasonable prices that I never considered it.
My primary goals in choosing filters, for two homes and our camper, are reputable company, 2 stage filtering (coarse & HEPA) replaceable filters widely available.
We have a whole house filter, then HEPA filters in the main living space (open) and each bedroom. In the guest room we only run it when it is used. Each purifier is sized for the space it covers.

Regarding your comment "One thing I have heard about the filter and box fan solution is that pushing air through a good filter can overly stress the fan, since it’s not built for that, and be a potential fire hazard. Has anyone else heard that?"
I have heard that certain filters may damage the unit. But I would guess that a dirty filter also does damage to the unit!
I researched and use a quality filter rated 4 out of 5 for air flow in my apartment. Apart from catching certain things, I have also noted much less dust with it...and that means less dust going back into the unit
I have read that one should check with the manufacturer for the maximum MERV rating allowable for a unit.