is there really a major need to know the details on individual employees anyway?
Yes or course there is. Lets say I have a customer in the US who has a colleague in the UK that also wants to buy my product, how can I put him in touch with someone in our London office without knowing their phone number? What if I want to grow my business in China and want to look at who the top sales guys are all over the world? Those examples are trivial but there are thousands more.
Yes, there would be some additional overhead from doubling up on personnel management rather than centralizing it all in one location, but it would just be an additional cost for doing business in that country, and one that I wouldn't mind seeing them pay (and I'm even an American, but I don't wish this surveillance state stuff on anyone else, so kudos to them for trying to discourage the export of their citizen's personal data).
That sounds lovely until you realize that the EU classes everything as personal information. Its a mess as it is having to get permission from every employee in an EU country to be able to share basic stuff like phone numbers and office locations outside the EU. I can't imagine how complex it would get if you then had a tax liability on top of it.
What will end up happening is one of two things, people will only ever host data in the EU (since it costs money to take it out and the EU is a big market so screw it, lets just leave it there), or companies will never store information there.
Actually thinking about it this could be a genius plan, effectively forcing companies to manage their operations in the EU by applying an export tariff (which is what this tax would be) that is so complex to manage its just cheaper to move operations there