I dont think Ill delete my Coinbase account, but I dont keep a lot of money there because its always a risk. We must remember that storing funds in the account can lead to their loss.
I don't feel like the safety of your assets is at the core of the (current) problem, but rather the safety of your personal identity.
both of them are current problems. in fact whenever you give up control over your private keys, it means that you are putting your "money" at risk because now Coinbase can do anything they want, from running away (worst case scenario) to simply closing your account because they didn't like your activities!
the privacy (personal identity) part is the obvious one since the service is located in US and is operating under US laws.
Third-party custody is for obvious reasons (no need to school me on those reasons, thank you very much)
a problem but is something you have to take into consideration if you're planning on using any third party service that involves exchanging your cryptocurrency. The premise of this topic is the #DeleteCoinbase controversy and third-party custody is not the reason why the #DeleteCoinbase hashtag started circulating over the internet in the first place (despite it being a big issue when using these services but that's besides the point here).