PCR tests can come back positive for several months post-infection, so there may be no point in testing people in that post-infection period, because it will come back with too many false positives to be useful. 180 days sounds long for that, but people do test positive for months sometimes.
The reason you can test positive for so long is that it takes time for remnant RNA from the virus to totally leave your system, and even though it's not replicating (you aren't infected or infectious), the PCR test is just detecting the RNA.
… which is a good argument for antigen testing (as your entire pre-entry testing regime, or in conjunction with a positive PCR history).
The other difficulty (impossibility?) is in segmenting the chronically infected vs those that are just working out the remnant junk of their recovered infection.
Pointless pedantry, just because I've been watching TWiV: the PCR test is detecting virus RNA because coronaviruses have RNA, and there's no DNA there. The rest I absolutely agree with.
More pointless pedantry from TViV, as I listen frequently as well: the hosts always point out that RT-PCR tests for the presence of viral RNA, but viral RNA particles being inside your nose or mouth doesn't necessarily mean they are infectious. The scale of CT values is 0–100 and lower CT values means more RNA copies. This is used a proxy for infectivity, though it's not terribly scientific. Furthermore, CT values are rarely (if ever) included on the test results.
The reason you can test positive for so long is that it takes time for remnant RNA from the virus to totally leave your system, and even though it's not replicating (you aren't infected or infectious), the PCR test is just detecting the RNA.