I think this is only the address one gives freely to the vaccination/test center and which is not checked by anyone.
I still can't think of any case where it would be useful in conjunction with your vaccination status.
I agree with you that it's not useful information for the purpose of a "health pass" used to gain access to venues and events. On the other hand, as a matter of Covid response strategy and enforcement of any restrictions (so for the authorities at large) it is very useful to know where a person that has tested positive lives.
It might have been useful in this case but the French government itself is not allowed to have a general-purpose database of citizen's addresses. Even the address that the social security has for contact purposes cannot be legally used for this (and is probably unreliable anyway as people forget to update their address when moving) and I don't think many people would have been comfortable with communicating their addresses for the purposes of Covid tracking.
One problem we're having in this pandemic is the squeamish and "can't do" attitude on about everything.
Name and DOB are reasonably needed to assert the person's identity. Especially in France everyone carries an ID card so people can show ID and certificate together.
Safeguarding private information is important but some must be disclosed as necessary.