This argument seems exactly backwards to me. If working abroad or using foreign services is difficult due to bureaucratic incompatibilities, then of course less people will do it. Anecdotally, I've certainly used foreign services where I had to ID myself and happily welcome any change that makes movement easier.

There will always be irreconcilable language differences and people do have a preference for staying in their birthplace, but that is no reason to not improve things.

I'm more worried about the EU actually implementing this well, but time will tell.