Ubuntu Core is intended for 100% unmanaged operation. It's the base upon which you install snaps to form a robust, secure, self-updating appliance that doesn't require a human to maintain it.
While you can try using Core like a standard server, be prepared for a bit of culture shock and a learning curve. It's not a complete, full-featured Ubuntu Server out-of-the-box. It's the minimal base upon which you add your various service snaps.
Ubuntu Core is an excellent host for a container hypervisor. It works best if the hypervisor comes as a Snap package. LXD containers on Core, for example, feel and act like server VMs. I have hosted many different kinds of servers in those containers.
As part of "secure" Ubuntu Core needs an SSH key for the first boot so you can login. That's why your key needs to be at Ubuntu One -- so the Core system, upon first boot, can download it. After your successful first login, Ubuntu Core does NOT dial home for key ever again. You can promptly delete your SSO information, change your keys on the device, or change your ssh settings to passwords instead; whatever you like. Best practice is to retain key-based access for the admin only, and build other accounts (and their access) in a classic Ubuntu Server (or similar) container.