Earlier quoted context omitted.
People stop very fast when people they know start to get sick and die.
When that happens, it's too late. Between the incubation period and the time to death it's about three weeks. At a 20% increase per day that means that even if you stop going out at that moment deaths will be multiplied by 46. If the rate is 30%, the multiplier is 247.
Current measured growth rates are closer to 15% per day (5 day doubling time). And people's behavior changes not when people die, but when people get sick. Which happens (depending on your sensitivity) only 1-2 weeks after exposure.
But the basic principle still applies. We are trying to buy as much time as we can to ramp up emergency provisions. And are trying to avoid overwhelming emergency rooms. By the time people's behavior modifies through direct experience, it is too late.
Making this concrete I live in Orange County, CA. Population, 3.3 million. Hospital beds, 6600 (source https://www.hasc.org/orange-county). I don't know how many ICU beds, but https://www.accjournal.org/journal/view.php?number=630 suggests it likely is about 6% of the total. So about 400ish.
Now walk that backwards. 400 people in ICU beds probably means 4000 people with symptoms means less than 0.1% of the population with COVID. Except that it is worse than that. We have those beds for normal stuff that goes wrong. They aren't actually empty now.
Long story short, we start piling up excess dead bodies due to lack of capacity long before most of us personally know anyone who actually shows symptoms.