For comparison sake, a 20 inch box fan, which many CR filters are made from, consume 60-85 watts depending on their speed, which is 50-100% more electricity.
This could be improved by finding more efficient fans, but if you're going for the cheap $25 fans at your local big-box store, you'll pay more for it over time in electricity costs.
I have one as well, but I live in a geodesic dome home and use it in the largest open portion of my house.
The ceiling at its highest point from the lowest point is 18 feet up, and the open section is about 1/2 of my entire home, so the one 20" fan keeps air circulating and being filtered for an enormous portion of my home.
If you live in a more typical home, the 20 inch box fan CR filter might be overkill.
The $2 PC case fan wins on both price, power consumption and quietness, and seems able to filter a roomful of air in an hour or so.
You must have very clean air already if such a puny fan would be able to keep particulate levels within acceptable limits. In winter, my Xiaomi purifier with a quite powerful turbine fan (or whatever those things are called — they're optimized for pushing air through dense filters) is barely able to keep PM2.5 within 5-10 micrograms on max speed (with doors and windows closed). A PC fan would make approximately zero difference, on or off.
You will spend a bit more buying a few of them, a 12v power adapter, and the shell to tie everything together, but you are correct.
If you buy the cylindrical air filters, you can pop one on a table, pop a case fan on top, and hook it up to a phone charger via a 20 cent Usbc adaptor.
As a bonus, the USB-C PD adaptor has selectable voltage (5, 9, 12v) on little dip switches, and that can be used as a speed control for a 12v fan.
Turn it up to max when cooking, and down to silent again when sleeping.
No need for any fixings or case or anything.