I assume that you are using a small hobby level compressor without any particular air filtration. That will suck tons of airborne bacteria and mold spores/fungi into your system not to mention that it's usually contaminated with oil vapor, condensate, rust and micro scale debris detaching from compressor tubing unless you use staged filtering with pre- and coalescing filters to remove it!
That is of course dependent on the state of the compressor unit. Since you keep doing it, I assume you either have a high frequency maintenance schedule for your loop so that any possible side effects from using the compressor won't be seen or that you are very fortunate to have a device and an environment that promotes success in using it.
Your assumption is wrong. I work on my classic car over the summer months so have a modest 50L 2.5HP compressor in my garage, not as large as I'd like it but I don't have the space or a 3 phase supply in my garage

. The airline is split in two; one airline is raw dirty air straight from the compressor and the other goes to a filter regulator to catch the oil, moisture and other detritus so it doesn't harm or corrode my air tools. The quality of the air might not meet the standards you mention above but it serves me well.
As for a high frequency maintenance schedule for my loop - that really depends on how often I change a water cooling component - which isn't very frequent. My last maintenance was only just recently for my project build and that coolant had been in there for about a year I reckon.
Now this is really going to make your teeth itch and your skin crawl - my reservoir is attached to my external radiator, which sits on my window sill, directly where the sun can beat down on it from mid morning to sunset. Apparently the ideal conditions for crap to prosper. I have some "stuff" at the bottom of my reservoir after a year, not sure what it is, but it's not alive; they'll be more life in the Chernobyl NPP than in my reservoir! I suspect the stuff in the reservoir is leechings from the flexible tubing which are the umbilical cords between the radiator and the pc. No amount of cleanliness would have prevented that.
I appreciate that your doing your research, asking questions and wanting to do the job right, but you have to set some limits. Those can be budget available, time spent, perceived benefits, possible savings, worthiness, and personal expectations. Is the juice worth the squeeze

.