I don't know either, however TI at the time also produced the "Silent 700" terminal series and it had the same font (all essentially upper case characters just some larger and some smaller.
Perhaps it was an early example of the DRY mantra being applied incorrectly.
That was an unobjectionable comment, so I guess the downvotes are a stimulus to try to get me to write more. The Wikipedia page for the TI-99 mentions the "small capitals" but does not link to the page I linked to. So some people, at least, who read that page won't get the reference to the typographic tradition (if that's what it is).
A larger issue is the idea that, by choosing a small caps style for their font, TI were acting inexplicably or irrationally. It is worrying but not surprising that the HN crowd finds it disturbing when a company makes a creative decision that doesn't have a clear business case behind it, while being completely innocuous, and which potentially could have helped to differentiate their products. It's the typical negative engineer stereotype coming through: "No imagination or creativity allowed, except if it's to solve a specific problem".
That Wikipedia page you linked to explains that small caps are used almost exclusively to emphasize or distinguish text from text set using the usual mix of uppercase and lowercase letters. So pointing out that small caps are a well-established typographical practice does nothing to explain what TI was thinking by including small caps but not lowercase. And no matter how innocuous you consider it, it is clear that the decision strikes many users as odd, and that it comes across as something of an unattractive technological limitation, akin to the then-recent systems that only supported uppercase.
It's slightly complicated, but the smaller caps of "small caps" are the lower case. As Wikipedia says, setting text in small caps is "technically not a case-transformation". In those days it would not be surprising that a system would only have one font.
I don't know about the Silent 700's font, but it looks to me like this probably wasn't a mistaken case of the DRY principle: after all, the TI-99's lower case letters are still stored as separate bitmaps (they are reproduced in an image here: http://electrickeet.com/line-itfont.html).
So it is clear, at least, that they had the storage for lower case, and for whatever reason decided to go with a small caps font. It isn't a result of a simple limitation that they hacked around by scaling bitmaps or something like that. I wouldn't like to speculate about what fraction of users found it odd at the time.
Perhaps it was an early example of the DRY mantra being applied incorrectly.