When developing a distributable Theme, does it HAVE to be “inheritable”?

However, in the event that it becomes appreciated to the public – does it necessarily HAVE to be inheritable (the ability to have Child Themes derive from it)?

While you can certainly make life difficult on users who try to use your Theme as a template for a Child Theme, it is all but impossible to prevent your Theme from being used as such.

Am I right in guessing that there is some publicly available Themes that are filed under some sort of “non-extendable” category?

What do you mean by “filed under”? Who’s file system? Who’s categorization? WordPress itself makes no such categorization. It simply uses Themes if they exist, and are valid – whether stand-alone Themes, or Child Themes using a template.

Is there any particular reason that you would want your Theme to be unable to be used as a Child Theme template?

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