I think it makes sense to isolate anyone who tests PCR positive for coronavirus, right?
Also, is it 100% sure that asymptomatic people will not transmit the disease? What if they are just pre-symptomatic? Where do you establish the cut-off?
Asymptomatic is being used as a different classification than pre-symptomatic in the literature. Asymptomatic means you never develop symptoms. Pre-symptomatic means you haven't yet but will. Pre-symptomatic phase is not long though. Typically just 1-3 days, I think, from the latest literature.
Given the tiny window of time that exists when people are infectious and might not know it, and given the very low likelyhood of a PCR test being done in exactly that time, and given that PCR testing has a lot of problems (e.g. triggers even if your body has destroyed the virus), and given that nurses and doctors are pretty important, I can't see it being useful to actively test in hospitals. It's everywhere by now anyway.