The other point is that banning exercise would push people to make unnecessary trips to the shops, increasing the risk of transmission even more
Then you get the law of unintended consequences. If too many people are shopping the law may have to change to ration the days and times people can shop - which also requires people to produce a multitude of documents and paperwork, and diverts valuable police resources
Basic point is that without a national ID card or compulsion to carry proof of address - which would require major legislative and cultural change - the gov cannot enforce additional restrictions. The key to stopping the virus is to ensure people obey the current rules safely.
