I believe the main miscommunication here is that you think of the Plasma clipboard as an application - like the GNOME extension or “clipboard managers” for Windows or Mac.
But this is not what the Plasma Clipboard is - the Plasma Clipboard is the actual clipboard thing of Plasma: when you press CTRL+C, this is the thing that holds the copied text (or image, or whatever you copied). When you paste - the Plasma Clipboard is what is providing the thing to paste. Unlike other operating systems, in Plasma the clipboard has an icon that shows you stuff and let’s you configure extra clipboard features that Plasma offers, and if you don’t like to use them, you can disable the clipboard icon but you aren’t allowed to disable the clipboard itself.
If you may ask - why is the clipboard icon not disabled by default? The answer is simple - the Plasma team thinks more people should know about the marvellous features that the Plasma clipboard offers, and if the icon is disabled by default then users will not found them very easily, if at all.