Every state has their own tax scheme. Every new employee in a new state is a big set up cost and ongoing maintenance.
Then there's the potential for each employee's address to be considered a nexus, since each of their homes becomes a de-facto company presence. Potentially subject to local registration, licensing and taxation by local municipal authorities, in addition to just the state level requirements. If you have a presence in the state, and your employee's official work location is that location, then you only have to deal with that local registration once wherever the presence is located. But if you don't have a location the state, or you have employees who are officially designated as work from home (rather than unofficially working from home while being designated as assigned to an office), then this quickly scale into a giant mess of regulation to navigate[2].
[1] https://taxfoundation.org/local-income-taxes-city-and-county...
[2] https://smallbiztrends.com/2018/04/remote-employee-complianc...
[1] https://smallbiztrends.com/2018/04/remote-employee-complianc...
-- Yes, you can outsource most of the payroll-related headaches to someone like ADP but
-- There are still a lot of other state by state details that can't just be handed off to a third party and told "Make it so." It's not a particularly big deal for a larger company, but it can be a fair bit of overhead for a small employer adding a new remote employee in a state with lots of paperwork.
The employer needs to pay social contributions in the employee's residence country. And more often than not, the employee cannot just become a freelancer or incorporate a single-person company and bill only one customer, as this is considered disguised employment. So no, it's not necessarily trivial for an EU company to hire a remote worker somewhere else in the EU, unless they have a local presence already.