1) Severely reduced in-take of new patients of patients due to lack of beds available (and longer COVID recovery time)
2) Reduced ability to effectively care for other patients due to limited beds and transmissibility of the disease, and workforce reductions as healthcare workers get sick (this is not a hypothetical, this is happening in the hospital my wife and brother work at).
3) Forcing healthcare works to perform their jobs without subsequent PPE for their own protection, increasing their own health risks and creating serious issues for mental well-being when working in this environment day-in and day-out.
The healthcare system is designed to treat patients. Believing the system is not exceeding what it can handle because somehow "the system itself" is not damaged (which I'm not even sure what you mean by that) but dismissing patient care and outcomes is like evaluating a vehicle's crash rating, but not evaluating the damage to the vehicle occupants.
Secondly, that is exactly what triage is! People die, doctors are trained to decide of a group of people which are dying, who has the better chance of not dying.
I would be interested in seeing if there is data to say whether being put in the ICU actually _increased_ risk of death. Of course this would be hard to prove as only the most sick went to the ICU etc.
I think your definition of "what they are capable of handling" (for some reason I can't reply to your other clarification of this definition) isn't one that many people would think is a good one. It may be technically correct in some domain, but this isn't it. Healthcare systems are there to provide healthcare for people, and if they can't do that (as in this situation) then they are incapable of handling it. In addition (in the UK at least, can't speak for anywhere else), this has led to not only ICU capacity being exceeded, but also routine healthcare being diminished - either because of people being unable to visit a hospital, or unwilling to do so.