I feel like skating would be a lot more popular here if you could show up any part of the day save a few intercessions for smoothing the ice. Or perhaps a private rink for practice and one open all day for the public.
Most rinks in the US, especially in less populated parts of the country, have a single ice surface.
The rink management earns a profit from precontracted rentals to hockey groups, from public sessions that reach at least, say, 20% of capacity (i.e., more skaters than would be allowed on a freestyle session for safety reasons, but at lower entry fees), and group lessons.
Practice sessions for figure skating are more likely to be money losers, but in most cases better than leaving the ice empty, and there are other advantages to working with a figure skating club.
Rink owners are generally in the business of making money, and figure skating programs have to negotiate ice times and prices that will accommodate both their members' needs and the rinks' requirements.
There would need to be at least one extra ice surface in order to run public sessions all day long and still have ice time available for hockey, figure skating, and group lessons. Locations that can support multisurface ice facilities will generally also be able to support participation by higher numbers of hockey teams and figure skaters, but not 10 times the number of casual users, so using only one rink for both those sports and leaving the other one open to casual public skaters all day long would generally not be an efficient use of ice time for the rink or the steady users.
Some cities -- usually in locations with moderately cold winters -- have outdoor winter rinks that are available to the public to walk on for most of the day. These ice surfaces tend to be much smaller than NHL let alone Olympic size.
That kind of seasonal rink can be useful for getting more members of the public onto the ice, but they're not useful for hockey or figure skating training.
More to the point, those rinks are generally not near and not affiliated with indoor rinks used for regular training.
There isn't one person or organization who could say "Let's make figure skating more popular by opening a rink that's open to the public all day long."
And the process is just too disorganized. Do you have to pass levels in other countries?
It depends on the country.
I remember wanting to compete. I got really good in a summer. And the "testing" format for USFS was sort of maddening. You can't just look up what you need to do to pass each level. You like... have to log into a USFS account. So if I'm new to skating and think "wow I progressed pretty well this summer, I wonder if I could compete this fall at a certain level" but you have to pay dues to even see the evaluation criteria? Don't even know what/when/where you can compete? It's just horrible organization.
I agree that the current design of the US Figure Skating website is not welcoming to interested parties who are not yet members
(or all that convenient for members either).
However, if you are interested in testing and competing, you should be taking group or private lessons from a coach who can point you toward the requirements, as well as letting you know when it's time for you to join the organization. At entry levels, coaches are often the best guides toward entry.
If you want to know what skills you would need to pass the first levels of USFS tests, or to enter in a competition level that does not require tests, you can ask in the Lutz Corner section of Golden Skate, and other posters will be happy to list the requirements for you and share links to relevant documents and videos.