If that checkbox was all that held me from "full freedom", then I concede your point.
Today, if I'm a consultant and have a consultancy company registered in EU country X, if I come to EU country Y to provide my services there, it's pretty likely that I will have to set up a separate company in Y or Y's tax people will be after me (that's currently the situation in UK for example).
In a real single integrated market, I'd have company registered in country X, serve customers across entire Europe, but file taxes on the entire income in X only. I'm thinking they don't allow that because it would open doors to all kinds of tax optimization for the little people - ex. say UK workers would register themselves as companies in countries with very low taxes, and continue to work ("provide services") in UK. This kinds of schemes are allowed for the megacorps, but not for us regular folk.
Hardly a cumbersome experience.
Also, there are perpetual costs of having a company registered (such as monthly payments to an accounting company which handles paperwork, health care contributions etc.), so if you move around regularly between a couple different countries, you'll probably need to maintain a legal presence in each one, and thus have these costs multiplied.
it makes the statement "four freedoms are indivisible" somewhat hollow, because there has never been full freedom of services