Out of experience in Hong Kong, this is exactly what happened. People weren't afraid of testing positive, they were afraid of being taken away to a poorly maintained quarantine facility for two weeks. Even your close contacts would be quarantined for two weeks, making it so that many people (unsurprisingly) lied about who they met, or where they went.

For people, who live paycheck to paycheck, this would essentially destroy their livelihoods. They would be out of money (since they won't get paid for weeks), could potentially not feed their families, and are at risk of losing their jobs.