Given that monkeypox disproportionately affects gay men, your proposed policy would require the government to somehow identify that population, engage in regular mass testing of them and then actively police them to prevent them going out and infecting other people. Remember that tests have false positives. Many of the people who tested positive for COVID had no symptoms at all, or symptoms so mild they'd hardly noticed, so you can bet that mass testing for monkeypox would yield some steady stream of FPs as well.

You really think that's going to happen? If you think our governments would even countenance that policy for a second when it'd disproportionately impact LGBT people then, well, you don't live on the same planet as I do!