Vaccine-induced immunity is better because it comes with drastically lower chances of serious illness or death than the actual infection.
There were plenty of studies comparing immunity through infection and vaccination pretty early on. One interesting aspect initially was that it looked like the combination of vaccination and infection was particularly effective. The infection acted like a booster.
I'm not familiar with the exact handling of this in the US, but in general it is difficult to count infection as a replacment for vaccination. There is likely much more variability there, there was less data about this available and the simple tests for COVID are not that reliable. Not impossible, but far more complex than requiring vaccination.
There were plenty of studies comparing immunity through infection and vaccination pretty early on. One interesting aspect initially was that it looked like the combination of vaccination and infection was particularly effective. The infection acted like a booster.
I'm not familiar with the exact handling of this in the US, but in general it is difficult to count infection as a replacment for vaccination. There is likely much more variability there, there was less data about this available and the simple tests for COVID are not that reliable. Not impossible, but far more complex than requiring vaccination.