It's absolutely not solved. I run a company with employees in multiple states.
The payroll company takes care of some of the problems, but for example, every state has different rules about worker's comp. Most states require you to get your own, but you still have to let them know. Some states require you to buy into their state system, which requires signing up.
Then there is corporate registration. Many states require you to register as a foreign entity. Payroll doesn't take care of that.
Then you have to pay state taxes, or if you just have employees, you have to file a form that says "I don't owe your state any income taxes".
There are other things different states do differently that the payroll provider doesn't take care of.
For what its worth payroll companies like that do exist, but they generally only work as staffing/funding companies - you pay a markup and they manage workers comp pools/state legal issues/etc (though most only have regional not national support) - unfortunately that might be worth 1.3-6% of your payroll :|
The payroll company takes care of some of the problems, but for example, every state has different rules about worker's comp. Most states require you to get your own, but you still have to let them know. Some states require you to buy into their state system, which requires signing up.
Then there is corporate registration. Many states require you to register as a foreign entity. Payroll doesn't take care of that.
Then you have to pay state taxes, or if you just have employees, you have to file a form that says "I don't owe your state any income taxes".
There are other things different states do differently that the payroll provider doesn't take care of.