That's indeed fascinating. Any such line will always have an element of arbitrariness. I.e. Pick duration Y. Then why not Y+1 or Y-1.
That being said. Pandemics are highly predictable and where I live (Europe) we had the benefit of seeing different approaches being used by different countries with varying degrees of success (Taiwan v. Italy).
There are measures (such as air travel restriction) where we know they're not that effective (although they do buy you some time). There are measures (such as social distancing and being early and aggressive in closing schools and other facilities) that are known to be more effective.
I think the line can be drawn where one has sufficient information to act quickly and still refuses to do so.
In government's (limited) defense. Exponentials are highly counterintuitive, so it's understandable the right thing feels strange.
The right time to implement measures is precisely when everything 'feels fine'. That, coupled with political blowback and economical impact serves as a constraint to quick action IMO. [1]
I'm by no means an expert in this field. I merely study human behavior in the context of business. So with a little luck, an epidemiologist will chime in.
[1] I suspect that there's 1 other bias that plays a role. Namely, what doesn't occur is harder to quantify than that which does. E.g. The FDA might pull a drug and save lives as a result. On the flip side, the lives that are lost because certain drugs take years and years to market are hard to measure. There are virtually no consequences for The FDA regarding the lives that are lost by being slow. There are massive consequences for the lives that are lost by approving a bad drug. Now imagine that the harder to quantify lives lost due to slowness exceeds those due to bad drugs. That would mean The FDA had a negative net-effect yet it would feel positive due to this bias.