- With positive pressure, the intake air doesn't pick up contaminants from the wall cavities and other nooks and crannies within the building envelope.
- A fresh air supply fan can be fitted with a high-quality filter (HEPA or near-HEPA) to supply air with approximately zero PM2.5. (This is a very, very effecive way to get indoor air that is cleaner than the outdoor air without substantial power consumption.)
- You can open the door without moving the fan! You can leave it on with the door open! And it may improve the air quality in the rest of the living space more than the under-the-door scheme.
In a very cold climate, it might make more sense to put something like this in a different room so that the unconditioned supply air could be mixed with conditioned indoor air farther from where anyone is trying to sleep.
For what it's worth, there are a couple vendors of paired decentralized ERVs that alternate which one is supply and which one is exhaust and blow all the air through energy recovery cores that buffer both temperature and humidity. They're intended to be installed in holes in the walls, but it ought to be possible to fit them to windows or trickle vents with some creativity to operate them without any permanent modifications to the structure. In a climate with serious weather, energy recovery can substantially improve comfort and efficiency compared to using unconditioned supply air.