Even outside of privacy issues, Coinbase goes down during critical periods often. Price crashing and you want to buy/sell quick? The site will likely be down.
Outside of accessibility issues, Having Bitcoin on coinbase is more like an I-O-U and defeats the purpose of cryptocurrency imo, which is having the private keys to your funds which only you control.
I recommend this guide to set a multisignature wallet through CoPay and Glidera. And managing your keys with a password manager like Enpass.
https://gist.github.com/paOol/d6c78c339cc5c4df6dd745d3bc2cc5...