I'm not sure about remarkable, it's a quality of implementation issue. Around the turn of the century I worked on an EU project where we did this for voice calls with IPv6.

In the present era QUIC can support doing this, although whether that'll be something every popular implementation actually does remains to be seen, but again a high quality implementation will be able to just rebind - "Hi, this is still me, I just have a different network address now" and carry on seamlessly.