I suspect many people would still voluntarily use masks, self-isolate, protect their eldery and take other precautions.
It would have spread very rapidly, overwhelming health systems utterly. Do you remember the mask shortage early on in the pandemic? Do you remember the oxygen shortage recently? Have you heard the news about nurses and doctors quitting because of burnout? Imagine all of those dialed up to eleven, all at the same time. Along with shortages of cleaners, orderlies, and basic hospital supplies.
Nearly all the people whose lives have been saved by treatment in intensive care units would be dead, and many more besides: accident victims, cancer patients, etc., etc.
The sickness could have spread rapidly enough that essential services were entirely out of action for long periods of time . No water. No power. No air traffic control. No road repairs. No trains. No food transport. All of these at the same time, for weeks.
In hindsight, I suspect the biggest factor was not whether it was compelled, but whether people could afford it. (Plenty of payments to stay home or keep workers home were still made in Japan and Sweden.) If your rent depends on providing black market haircuts, you'll still perform them despite the ban. And if you're allowed to do haircuts, but the government will instead pay you to stay home to avoid the epidemic disease going around, maybe you'll just stay home.