but you never refer to an 8th note or a 10th note. I've never heard of anyone referring to anything but a 9th and 11th above 7th.

[Useless Music Theory]
To be completely technical, this really depends on the terms you're using. If you are simply talking about "intervals" (the distance between two notes) then there's nothing wrong with "8th" or "10th", but (as you point out) this really isn't the information people are trying to get across.

When speaking about "chords", however, 8th and 10th make no sense because you'd just use the numbering from the first octave. The difference between a 2nd and a 9th chord is that a 9h implies that a 3rd 5th and 7th are also present in the chord (the key note being the 7th, as any chord implies the 3rd and 5th). An 11th also implies the 7th as well as the 9th preceding it (though it's not strictly necessary). A 13th is another chord I see sometimes, BTW.

Practically the way this works out is that if I see a 2nd chord (although to be completely technical, this isn't really a chord but a suspension), I’ll just play a regular chord with the 2nd added. If I see a ninth, then I’ll add the second, but also a seventh as it’s implied.
[/Useless Music Theory]
I don’t believe any of this relates to the task at hand, however. I just like to talk about music theory.