There are labs that guarantee < 72-hour turnaround times for travel. It costs extra but hey, that's life. This pandemic has been around for a year now so if it was that important to travel, it's worth paying extra for the test.
In Central America - could vary a lot by country.
You're telling me there are no private labs that'll do it quicker? We have plenty in the Bay Area. Sounds like a market failure.
72 hours is a system problem, not a fundamental timeframe for the test.