It's definitely really important that a portable database format that can be persisted on disk be used for the wallet file database, or else you couldn't move wallet files around and they'd (for the most part) be stuck on the system they were created in. So the options are one of BDB and sqlite3 which achow101 already mentioned.

Obviously any change in the database used for wallet.dats will be rejected since it will break compatibility with all tools that depend on the structure.

First off you wouldn't want to use a SQL database for any bitcoin data because you'd have to shoehorn the key/value data into relational format with tables, primary keys and all that special stuff. This leaves only NoSQL databases as a viable option, and wouldn't be end-user disruptive because nobody moves around the chainstate database.

Usability also has to be considered to e.g. we don't want to require people to create a Postgres database and user and password at first run for Bitcoin Core to use.