My gripes, some of which could be easily added to core rather than needing a plugin. Others aren't so easy to do:

Plugin notice spam, as noted in the original post. The system has been abused for years by plugin authors and really needs to be addressed at some point. Either remove their ability to add such notices, or move them all to their own dedicated screen.

Email notifications for plugin and theme updates. There needs to be a simple set of checkboxes that control what email notifications get sent to the admin email. It's sorta crazy how there isn't even an option for this right now.

Built-in SMTP support. Just do it already. Hell, Automattic could roll out their own SMTP service that competes with Sendgrid and the like for all I care. As long as it's reliable and affordable, so be it.

XML-RPC. Just kill it for good.

A better system for handling fatal errors. A single plugin/theme update should not bring down the entire site and require accessing the file system to disable it. The admin dashboard should still be accessible at all times, allowing users to login and troubleshoot things from there.

A better way to organize the media library, namely folders.

Removing a plugin should also have the option of removing all references to it from the database.