The “no non-COVID patients” part didn't happen because suddenly no one needed ICU care or other hospitalization for non-COVID reasons, it happened because people were systematically excluded starting with methods from soft (discouragement to seek care) to hard (bans on classes of procedures, triage prioritization, etc.) from hospital care for non-COVID reasons.
Hospitals in and around NYC were, like those in Italy at the peak of the crisis, using criteria beyond medical need to allocate ventilators because medical need exceeded supply. That's overwhelmed, and ant standard which suggests it isn't is a dumbass standard.
Maybe your threshold for what counts as ‘getting health care’ is different from mine. For me it amounts to more up than just being physically in a hospital. If the people described below were your family, would you be satisfied with their health care?
"Some of them, bless their souls, can't do anything for themselves," she said. "How can I take care of 14 people when I have one tech and they have 30 patients. It's so bad here you guys."
https://www.independent.co.uk/news/world/americas/coronaviru...
To me is seems straightforward to say that a system that is no longer able to provide an acceptable standard of care to a majority, or large minority if it’s patients, has been pushed beyond its capacity.