"Because no swabs are required, and no fancy equipment is needed, the tests are less vulnerable to backlogs"
That, sadly, is nonsense unless you have thousands of technicians available to process the tests. What we have here is a classic latency vs throughput problem. 45 minutes to an answer is a lot better than 24-48 hours which is about the best achievable with the PCR tests. But even if only a third of the 45 minutes is a tech messing with "pipettes, a heating source and an enzyme mixture" and the rest is waiting for reactions at best one tech could do perhaps 30 a day. On the other hand the "fancy equipment" in PCR labs can do thousands of such tests in one go (UW Virology here in Seattle is doing over 5000/day[1]).