Those fans will not have sufficient static pressure to be useful. These makeshift purifiers may be great in a pinch (wildfire season and stores are all out), but far from the best.
This is indeed the "conventional wisdom," but if you do the math it turns out this is incorrect.
The trick is to use high-airflow MERV 13 filters (ideally 3M 1900, which has high pleat count and low resistance) instead of high-resistance HEPA filters, so axial PC fans can generate enough pressure.
At that point, you’re not doing any actual air filtering. Just use them as fans instead.
Merv-13 means it filters at least 75% of the particles passing through it.
For a standalone air filter which is pushing the filtered air into the same room its drawing from, we can assume reasonably good mixing of the intake and exhaust air. Thus to be equivalent to a HEPA-filter it only needs 1/3rd more airflow... Which really isn't much.
This doesn't follow for a a fancier setup where you're taking dirty air and blowing it into a cleanroom or something... but that's not how we're typically using household air filters.
Is it safe to assume all particles are equally as likely to be filtered, or are there particles that HEPA will filter that a MERV-13 will never filter no matter the number of cycles?
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The linked PC-fan purifier has been tested and shown to purify air faster than the conventional alternatives, and are not makeshift, so I'm not sure what you are referring to.
From the specs it looks like they are probably closer to higher-static-pressure server fans, the CADR is a few hundred CFM and it pulls 30+ watts. And as with many of these designs, you can compensate for low pressure performance by increasing filter surface area... the greater the surface area the lower the pressure drop. Of course, the problem with this is you are just spending more money on filters, which is the expensive part.
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