The inline (html) ToC is the only thing that allows the "Go to ToC" feature to function (on at least the older Kindle devices). The NCX file is what allows users to jump to various "chapters" using the left-right arrows. I do believe the very latest Amazon devices/firmware allow you to navigate directly to the various chapters via an NCX view.
The latest
Amazon Kindle Publishing Guidelines (Sec 3.3) still heavily encourages
both the inline HTML ToC and the logical ToC (NCX file )—though only the logical ToC (NCX) is considered "mandatory."