Literally all developed nations had their hospitals swamped. In western europe this is no longer an issue since many have gotten vaccinated.
I remember reading that Arizona hospitals were "overwhelmed" but the only actual data I saw on that was a peak of 90% ICU capacity. There was a story about the maricopa county morgue being too full, but that turned out to be mostly bureaucratic incompetence.
The problem might be inefficient load balancing on hospitals, so even if, say, 80% of ICU beds are taken, you will get some hospitals that run out of beds while others have lots of excess capacity and an inability to efficiently share the load.
It would be interesting to get systematic data on this, together with some ideas on how to improve load balancing.
Yes, some places had temporary surges for which they were unable to cope, early in the pandemic. Wuhan, parts of Italy, New York, a few others. But it never happened in a systematic way. If hospitals truly believed that overcrowding were a looming threat, they would not be laying off nurses as they are in many American localities.