They also do not support 3rd party DECTs. I had to use a cable to my Fritzbox to be able to use a DECT with addressbook. When connected as a DECT, The Fritzbox will not transmit the addressbook to the phone.
Unfortunately, the DECT spec as implemented by many manufacturers isn't as broad as people seem to think it is. Most interoperability was done through DECT GAP last time I checked, and GAP lacks common features like "rich caller ID" and "address books".
I've seen other brands do address book support just fine, I think AVM tries to be compatible enough but just can't get the full feature set for every brand and model.
I've even seen Gigaset phones failing to support address books on more modern Gigaset basestations, DECT hardware is kind of a mess in that way.