The main difference of Cockpit as opposed to more old school visual server administration tools that it doesn't replace standard server management approaches with its own configuration storage in some weird database.

Edits which you make through cockpit and edits which you make through cli are exactly the same edits in same APIs. You do not need to choose one or the over. You can switch from one to the other seamlessly on a command by command basis.

Sometimes I like a web page to bring information to me rather than having to go on a command line use those tools to find the data I want. YMMV.

I use it for certain use cases, where it definitely is more convenient. For example, adding a new user or adding an ssh key for a user or debugging SELinux issues.

Web UIs are nicer to deal with for simpler tasks. You can use this on your phone easily. Less technical users can be instructed on how to perform simple tasks like remotely powering off a machine.