If people via a hardware widget strapped to them, I imagine that could create some regulatory hang-ups and class-action lawsuits via various state or national laws on information security, and that a lot would refuse to wear it anyway. Or leave it on their desk. Or find other creative ways. This would be true with phones too.
No. Wouldn't work.
Any virus that spreads thru moisture in the air that you breath and lives on surfaces for days can travel far more than 6 feet [1].
[1] https://www.webmd.com/lung/news/20200414/cdc-covid-19-can-sp...