When is the address indicated on a passport being used?

In theory, if you lose your passport and someone finds it, they could mail it to your address. Alternatively, if you have some sort of incapacitating emergency, somebody could contact you at the address. Here's an Australian passport's address page which makes this explicit:

In practice, this never happens. If you lose your passport while travelling, you need to make a police report and tell your embassy, who will electronically invalidate it as part of the process of issuing a new one. So there's no point to mailing around found passports. Likewise, if you have an emergency, your emergency contact will be contacted by phone, not by sending a letter.

This has not gone unnoticed, and addresses on passports are an endangered species these days: having an address in the passport is not mandated by ICAO regulations, and most countries' passports no longer have it.

Since the introduction of the 'International' Passport in the 1920's, passports should have a Domicile entry (Page 2 of sample passport, Annex 1 of 1920 Conference, page 156 of pdf).

The recommendations do not state the purpose or what this field should contain.

However since the general agreement about the issuing of visas states, as a general rule, that visas should be issued at the place of domicile of the applicant (a rule which still applies today), this is probably the reason for this field.

In German passports (former and present), only the city is entered on the Biographical data page.

FINAL ACT
adopted by the Passport Conference on May 18th, 1926.
...
RECOMMENDATIONS
SECTION I. - GENERAL QUESTIONS.
II . Facilities to be Granted.
...
B. Visas.
The Conference recommends:
...
(3) That, although as a general rule visas are granted by the diplomatic or consular authorities competent for the place of domicile of the applicant, the diplomatic and consular authorities may in cases deserving special consideration grant visas to persons not domiciled in their area and that as far as possible the said authorities shall not require the applicant to appear in person. In the case of transit visas, the applicant should only be required to appear in person if the authority granting the visas has doubts regarding the case.

Sources:

• 1926-05-18: Geneva Passport Conference (mirror)
• 1928: Hall’s Passport « Hall's Journals

I've asked the question to an employee at the French Embassy in Bangkok working on issuing new passports does accept: she couldn't think of any use of the address indicated on a French passport. So it's unlikely that the address indicated on a French passport has any major role, if any. lambshaanxy's answer gives the best reason I can think of, and Mark Johnson's answer seems to explain well the origin of this relic of the past.

Also, according to https://passeport.ants.gouv.fr/Questions-frequentes/Questions-pratiques/Je-demenage-dois-je-modifier-mon-passeport-ma-carte-nationale-d-identite (mirror):

Si vous déménagez, le changement de l'adresse portée sur le passeport, la carte d'identité ou le permis de conduire est facultatif.

Google Translate:

If you move, changing the address on your passport, identity card or driver's license is optional.