So if we have a country of 350 million, let's assume 35% aren't vaxxed. That's 112.5 million. Take 50% of that catching Omicron. That's 61,250,000. Multiply that by .005 and that's 306,250 people in the hospital due to the virus.

Add another (smaller relative) portion of vaxxed (another 55,000 or so) and you have 360,000 people more than usual checking into the hospital. Normally, hospital administrators try to run at close to capacity, because having unused rooms, unused resources is wasteful. So people who would be in with normal age related maladies, needing knee replacements, gall bladder and throw in emergency stuff like broken bones, car crashes etc. The 'system' is built for the normal load, plus or minus x%. 360,000 extra in a couple of months is a lot more than the normal load.