Also, it's not just tax implications. There's also complexity about time off (vacation and leave regulations differ a lot across the globe), conditions under which people can or cannot be fired (or hired), differences in terms of non-salary benefits that must be provided, etc.
A simple example of the hiring/firing thing: under French law, if someone is on maternity leave you can't fire them. You also can't hire someone on an indefinite-term basis to do their job while they are on leave. Hiring someone for the specific term of the leave seems to be OK. See https://www.globalworkplaceinsider.com/2017/05/do-employees-... toward the end, though the whole article is a great illustration of some of the differences in this area between French and US law.
And then there are the fun parts about general regulatory compliance. As a simple example I've run into, the US _requires_ you to collect and report data about the race of your employees (see EEO-1), while the EU _forbids_ collecting this data to start with, last I checked. So you have to have distinct processes for employees in different jurisdictions, your HR database needs to handle these differences in rules, etc.