I have seen models designed this way! Vornado used to make one, I think it's discontinued.

These directed-air "personal models" make a lot of sense to me... at least in theory. I haven't seen them properly tested.

The big air purifiers work great.. if the room is closed up. But their effectiveness approaches zero if you have the windows open or otherwise have unfiltered air entering the room. Which is kind of important, if you don't enjoy breathing in sky high levels of CO2. (If one's allergies are bad enough, or a wildfire is raging outside, CO2 might of course be preferable to particulates)