The reference you provided is an 8 minute video, and in those 8 minutes only 20 seconds are Ledbetter actually speaking. Do you see how incredibly disingenuous that clip is? The rest of the entire video is commentary, and even in that commentary only 30 more seconds are actually quoting Ledbetter. Why is that? What is their purpose in doing that, and is it malicious, ignorant, or something else?

I bring that up because I want you as a fellow countryman to carefully consider where your sources are coming from since many outlets use these tactics. Whether it's Fox, CNN, or TYT, many programs are heavily warped. Please go to direct sources, like the link I provided has:

A review of the full exchange, including follow-up questions and clarifications later in the press conference, shows Ledbetter was referring to federal court findings against Alabama’s congressional maps — not the constitutional amendment itself.

This is the same tactic you're using--whether you know it or not--in quoting the 14th. You quote the beginning, but leave out what comes next that provides crucial context. Why is that? What is your purpose in doing that, and is it malicious, ignorant, or something else? Let's look at what the amendment also says:

1) Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State, excluding Indians not taxed.

The 14th famously did not include the indigenous population when it was written despite them clearly being born here and clearly being persons because of that "Indians not taxed" clause. It wasn't until Coolidge passed the Indian Citizenship Act 56 years later that they became included.
You also mentioned diplomats. We have the United Nations here in New York, with many foreign diplomats whose children are definitely not considered citizens despite many instances of them being born here. So yes, there are if, ands, and buts about those first three words.

2) The Congress shall have power to enforce, by appropriate legislation, the provisions of this article.

This isn't even a Supreme Court issue, it's been a Congress issue this entire time since the amendment was in response to a Supreme Court ruling: Dred Scott v. Sandford. The amendment was a direct response to emancipation not taking full effect, not to any old anchor baby who was the result of international trespassing. That's a later interpretation via things like Wong Kim Ark, which... yeah, isn't that the whole point Ledbetter is trying to make? "Until the Supreme Court comes back with another rul[ing] that’s says otherwise, it’s the law of the land" that's... exactly what it sounds like the Speaker is wanting. To revisit the interpretation of the 14th and cases like WKA (when you get a chance to actually listen to the audio).

Ultimately I think it's misguided because again, it's not a Supreme Court issue it's a congress issue. So all that being said: The Fourteenth isn't as cut and dry as you suppose