Apparently, this is indeed allowed. Near its note about the $5 O'Hare fare, the CTA Fares Page says:
Tip: Use an unlimited pass to board at O'Hare for no additional charge.
The same page also confirms that at O'Hare you can buy a new Ventra card and put a pass on it, or buy a disposable one- or three-day pass. (Disposable three-day passes are only available at the airports and must otherwise be loaded onto a Ventra card.)
This TripAdvisor thread reaches the same conclusion, including an email from the CTA confirming that they say it is allowed.
As for why anyone would pay the $5 one-way fare instead of a day pass, the answer appears to be simply that until November 2021, day passes cost $10 and so there were more situations in which that was the right call.