>Aren’t all of the above equally capable of carrying and transmitting the virus?
No. If I had Covid a month ago and recovered then baring a compromised immune system or new variant I am not going to get it again this month. So I am not "equally capable of carrying and transmitting the virus" compared to someone who "had neither a vaccine or covid".
I understand that you would have antibodies and it be very unlikely if you carry the virus it would be unlikely to overwhelm your immune system in that time, but you can still carry/spread it right?
More directly related to the policy in question they can test you for antibodies, and maybe it is immaterial, but do they distinguish if you had covid 1 month ago vs 3 months vs 6 months? So does it work on the honor system or are they testing for antibodies, is it simply a matter of if you had covid at any point it doesn’t matter if you still carry antibodies you are not subject to quarantine?
No. If I had Covid a month ago and recovered then baring a compromised immune system or new variant I am not going to get it again this month. So I am not "equally capable of carrying and transmitting the virus" compared to someone who "had neither a vaccine or covid".