If you re-generate the password for each site, rather than sync, it means (1) you can't change your password on that site, (2) if any site puts in the effort to brute-force guess your password, they will have access to all the sites you visit.
The basis for Warrant Canary is that people publish an "everything's ok" message periodically on their project or website, so if the feds pressure them into creating a backdoor (as was suspected in the untimely death of TrueCrypt), they simply stop posting the "everything's ok" message. The untested legal theory is that the government can compel you to remain silent about proceedings via gag order, but they cannot compel you to state anything falsely. If apple pleads the 5th, it may set a precedent that's relevant to Warrant Canary cases.
This is not a good idea.