First, it's that hospitals effect on covid mortality is lower than believed. Second, while morbid, I assume mortality risk can be assessed pretty accurately by hospital staff. If you must triage, triaging someone who has a 99% chance of dying in the hospital and a 100% chance of dying outside the hospital raises the expected deaths by 0.01. Hospitals tend to serve everyone they can (for good reason) but the value add part comes from serving people who have a high chance of dying out of the hospital AND a relatively low chance of dying in the hospital.
These could be wildly wrong assumptions.
I would think hospital closures would cause a large increase in mortality rates as you don't get to triage effectively at that point.
I think the emphasis on ventilators at the beginning of the pandemic likely caused an increase in mortality in hospitalized patients. At peak panic, there was a big push to create and distribute ventilators, including open source projects, big name tech billionaires dedicating resources, etc. Then we realized these were actually damaging lungs further, and nixed that treatment, switching to oxygen supplementation only.
Out of curiosity, which mechanism are you thinking about that would lead you to the conclusion that hospital capacity doesn't impact mortality? The story that I have heard the most is that hospitals start to turn away people if they don't have beds from them, leading to either delay in care or no care at all. Both delay or no care lead to higher mortality. I cannot really think of a story where an over-capacity hospital leads to the same or reduced mortality.
If you believe that hospital closures lead to hospital overcapacity or delays in care, you can find some literature that shows that closing hospitals leads to an increase in mortality in the community [1].
1: https://www.nber.org/papers/w26182