Some places do it here in Finland. It works exactly as poorly as you imagine. People show up to work sick more often and spread their cold to everyone in the office, and doctors are bogged down having to write sick notes for 1-2 day absences.

Of course we also have a stupid parallel private employment healthcare system so these are doctors whose job description is pretty much doing nothing but this, so it doesn't (usually) directly lead to congestion in public healthcare -- but it does indirectly do that, because these are doctors who could be working as GPs or something else useful instead of what they're actually doing.

doctors are furious too

does it help that there's a shortage of general practitioners too? just give them more pointless work, that helps