As it applies to WDW, the rapid test takes too long to try and test everybody. It's 13 minutes per person plus the time to get the sample. The machine only does 1 at a time so you'd need at least several hundred at each park entrance.
Then there's the cost. I found an article that said the cost of the rapid flu test is around $45 per test. I assume that takes into account amortizing the cost of the machine. Neither Disney nor the insurance companies are going to eat that cost for everybody to get tested at WDW. Would you be willing to pay $45 a day extra to be allowed to enter? I wouldn't.
As someone who works in Florida hospital lab, I can say that you have all of this pretty much correct-
13 minutes per test, 1 test at a time per instrument, about the correct price per test (does NOT include the instruments, which we also run Flu A&B, RSV, and Strep Rapid on).
But what so many do not recognize is the rapid test is a complicated procedure with 3 minute warming period, a precised mixing time, and a 10 minute incubation, for which you need (in most states, FL being one) Qualified Medical Lab Technologists (someone with a MLT degree, certified and licensed by the state) to be able to administer these tests. These are not waived tests, and the byproducts of these tests can be highly infectious (since the test method amplifies the RNA in the sample) and said byproducts must be sealed and placed in large, leakproof, puncture proof, medical hazardous waste disposal units. All MLTs that are running covid on the analyzer, (and everyone nearby) are doing so while wearing a N95 mask, preferably under the BioHood. Not to mention all the maintenance, QA and QC that is involved in running these instruments. That's just the part I know.
There is also the collection of the swab specimen (an invasive and unpleasant insertion into your nasal cavity that I wouldn't want someone who wasn't a medical professional to do), not to mention the most important part- the ordering of, and resulting to, a qualified Doctor- who instructs you on what to do specifically, regarding your health, when you get your results.
This is just NOT something you can put in off to the side at bag check by the Parks.
I would imagine that when a park employee takes your temperature and the result does not match the criteria Disney sets, you'll be handed a flyer with the information of the 2 or 3 nearest hospitals or clinics nearby, and sent on your way with "have a magical day."
I'm sure the Disney Co has no interest collecting, storing, or having to disseminate any part of every guest's HIPPA protected "medical history" which is what they would be doing if they tested people before they entered.
No way.