I haven't encountered this with my personal email server nor heard of it from anyone else. I think this might just be an issue with Posteo.
It's easier if you don't try to move all at once. Spend some time looking at different email options and move that. Do calendar later. Get rid of Google Apps on your Android later still. Gradual change is much easier.
Of course it's possible.
The reason is clear: lock-in.
People are reluctant to change providers if they lose their mail address.
I think for .de domains, you are required to have your personal address in WHOIS if you are not a company.
First, I may be okay with it. And why would Posteo store WHOIS data? Unless they want to be a domain reseller, which is not what I asked them about.
Second, there are other TLDs.
I still insist that they do it because of lock-in and that they lie about it.
I think mailbox.org supports custom domains and is similar in other respects.
They should stop storing the mails themselves, they are full of private information. /s