Certainly the movement of people has added to the spread of the disease, but if we do away with "free movement" we'll still have movement: tourism, second home buyers, diplomats, lorry drivers, football matches, Olympic games etc. It's just that their movement will be hampered with border checks which don't include medical checks. I wonder if it would have made any difference. Apparently the outbreaks in South Korea and the Gand Est - the most severely hit part of France - have been attributed to big Evangelical conferences with delegates from all over the world. This sort of thing is going to happen anyway.
https://www.reuters.com/article/us-...is-center-of-new-virus-outbreak-idUSKBN20R1Q4This report is only 20 days old and look how few have been affected. (Last paragraph).