They're the only one that allows you to enter a second name via "care of"[0] in the address, and German postal services won't deliver mail if no name on the envelope matches the person registered at that address. In other words, you end up in a catch-22 where you can't sign a lease because you don't have a bank account, and you can't get a bank account because you don't have a legal address yet.

There are other ways to resolve this, but the easiest is "find a bank that will let you accept mail at the address where you're staying, even if you're not on the lease", and the only bank that does that is N26.

[0] I forget the German term, but basically

    Ms. Alice Foo
    c/o Bob Bar
    Baz Straße 14
    99999 Nowhere
    Germany

But yes, many banks want to send mail to your registered address only by default. They actually check your registration document.

[edit – wrong:] The German-language equivalent (that most young people won't even recognize anymore) is "z. Hd." ("zu Händen" – "to the hands of").

I haven't actually seen "p. Adr." ever in my life.