There is a massive amount of content for 5e that could be included. The player may be interested in using something that the DM has never thought of, or never even heard of. Your method, the DM pretty much has to say a draconian "core rules only", and even then a player could come up with a backstory that contradicts something in the setting.absolutely hate it. Lay out what is acceptable and isn’t upfront. That gives me the information I need in order to pick what to play.
Our way, if a player wants to play a Warforged Blood Hunter Harper Agent from Waterdeap, the DM can assess the character on it's own merits.