The first two [minimizing hospitalizations and preventing deaths overall] are the same.
No, they aren't. In the first case, if the hospital capacity exists then there should be no restrictions or precautions put out at all. In the second case, restrictions and precautions will last indefinitely until the entirety of society is vaccinated or the disease burns itself out.
We are not doing the third one [minimizing cases]
Have you been living under a rock? Virtually every metric and reporting criteria shifted from fatalities to cases about 9 months ago. No one is even talking about fatalities anymore, particularly the media, because the CFR has plummeted from ~10-15% at the onset of the outbreak to roughly 1-2% over last winter to roughly 0.5% now, a point where it wouldn't make scary headlines anymore because it's on-par with the flu.
The CDC's recommendation to re-instute masks (and the DOD subsequently following suit) is strictly based on cases, not an increase in hospitilazations or fatalities.