Why would you need to start a mailbox firm in every country with employees?
Lets say you have a German company and you have people working across Europe. For the sake of argument lets say that you have 15 people in France. Let say that all the people work for you 100% of the time, so they are effectively employees.
On the employment taxes/benefits front how are you paying the French state those 14 peoples payroll tax, and how are you paying in for their state pension? Pragmatically, you can't do this (AFAIK) without establishing a company in the jurisdiction and registering them as employees.
On the employment rights front, which jurisdictions are you following? As you have 15 people in France they are due to have a workers representative, does that fall under the French or the German system? If you have an issue with one of the team do you follow French or German employment law? Again, pragmatically each jurisdiction assumes that you fall under their employment laws and logically they'll assume you have a company in that geo.
Wrt jurisdiction, usually the employer's jurisdiction. You don't follow "employment law", you follow "international business" law or some such, because that's what it is.