[mcv]

I do not understand why a government service would require this. Governments should improve security, not undermine it.

(Then again, most governments don't seem to care much about what I think they should be doing.)

[sonnk]

The generated password is usually just random string and hard to memorise. If you need to use the password outside of the web, e.g. on telephone or in a physical office, then it makes sense to use a password you creates. This is similar to the "master password" used by password manager, you should remember it by heart instead of generating a random one.