I don't think this has to do with punishing the unvaxxed. It has to do with this:
The hospitals/ERs are already filling up and they are filling up with vaxxed people. Somebody is going to ask, "Why are the hospitals filling up with vaccinated people?" Without this EO the answer is, "Because the vax is making people sick." With this EO the answer is, "Because the unvaxxed aren't allowed in the hospitals."
I don't think this has to do with punishing the unvaxxed. It has to do with this:
The hospitals/ERs are already filling up and they are filling up with vaxxed people. Somebody is going to ask, "Why are the hospitals filling up with vaccinated people?" Without this EO the answer is, "Because the vax is making people sick." With this EO the answer is, "Because the unvaxxed aren't allowed in the hospitals."