Does Louisiana tax workers that haven't physically worked there? For example, if someone lived in Virginia but had remote contract work with a company based in Louisiana?

No, if you worked for a Louisiana company, but did not actually work in Louisiana (LA), you are not subject to LA income tax.  You would not need to file a LA state tax return unless LA state tax was withheld.  In that case, you would file a non-resident return that shows none of your income being earned in LA, and you would receive a refund of all tax withheld.