https://www.gesetze-im-internet.de/tkg_2004/__3.html
Translated "consist wholly or predominantly in the transmission of signals over telecommunications networks, including transmission services in broadcasting networks". I find it hard to argue that some piece of software can be a transmission service.
From the other hand, GMail was considered a "telecommunication service" by a German court:
https://www.noerr.com/de/newsroom/News/gmail-ist-ein-telekom...
Translated: https://translate.google.de/translate?hl=de&sl=de&tl=en&u=ht...
However there is an important difference:
"Google Inc. therefore has its own switching technology (original "Vermittlungstechnik" - transmission tech) and therefore has, in any case, partial control over the signal transmission."
An XMPP-client, in contrast does not have own transmission tech and has no control over signal transmission.
Please clarify what suggestion you mean: that XMPP clients are telecommunication services or that their developers need to register?
You don't trust the system, and you have good reasons for that, and the 'system' doesn't trust actors it does not control.
It is that simple.
But that is exactly what network clients provide: telecommunication services. IFF the relationship between the states and the governed was healthy you wouldn't bat an eyelash at the suggestion.
Problem is elsewhere.