In this case it seems like the steep price is to prevent frivolously using the emergency room. You can get covid tests dirt cheap (or free) if you schedule and appointment at a hospital or one of the testing sites. Emergency room has to have capacity to take on actual life threatening emergencies.
It seems like you've done the research here: how do you know how you are supposed(?) to do the test in the US?
Here in my municipality in Norway the media keeps repeating how/where/when to get tested, and if anything important changes the municipality will literally send a SMS to all its citizens to ensure as many as possible are up to date.
From my admittedly limited experience with the US (NYC/tri-state area) I get the impression that information is often hard to find and hard to understand. This could of course be caused by cultural or lingual differences since I'm neither American nor a native English speaker.
It may be hard to find if you aren’t use to it. Normally you would call your doctor/clinic and schedule a test for the next day or so. A lot of times you can get into an office for a test same day (this is how you get sick notes for school) although it may not be with your preferred doctor and may just be a nurse giving the test. For covid, since it’s so widespread, there have been testing centers setup almost everywhere and a quick Google should give you a list of the closest ones. Again you can always go to a regular clinic for testing but they may not have same day service.
The emergency room is the last place you’d go for a simple test. The only reason you should go to the emergency for a test is if it’s heart related or you think you may die (an emergency.)
