Just something to keep in mind

1. Custodial assets (stocks, bonds, funds etc) are segregated and generally protected in bankruptcy, UNLESS you have signed the securities lending agreement which authorises the bank to borrow your securities from your account for a small fee. In which case, your securities are lost if the bank goes in default. Worthwhile to check and revoke this agreement if you are worried about the institution.

2. Mortgage offset versus cash account balance, this is generally not standard case. There are clauses in your mortgage agreement that prevent this offset. You need to have asked the bank to take this clause out when you signed. Worthwhile to check.