What's up with unnamed elliptic curves in e-passports?
I don't have any visibility into the BSI standardization process, and so this is a guess; I suspect one of two things happened:


This is a potential way to deal with someone figuring out how to break both Brainpool and NIST curves (but not arbitrary elliptic curves; if they managed that, this hook won't help).  In that case, if someone did that (or if we suspect they might have), we can update the passports without modifying the spec or the readers.
This is a political compromise; some entity with political power pushed it into the BSI spec; possibly because they were card manufacturers that were already using other curves (and BSI decided they didn't want to endorse those curves for whatever reason); possibly because it gave someone a competitive advantage (our password validation equipment does it, our competitor's does not; forcing this in will delay our competitor) or possibly because some bureaucrat got it into their head that this was a good idea.


As for whether coming up with safe domain parameters is non-trivial, well, yeah, it's not something you'd want to hand off to an intern; however the known potential attacks against elliptic curves are well documented; it's not that difficult for someone who knows what they're doing to come up with curve parameters that make all known attacks infeasible.  In fact, there's this paper where they suggest literally creating a fresh elliptic curve for every single key exchange.