I agree that we don't need upper and lower case. In fact you may notice I did not include the 2 cases in my calculation of number of glyphs in English. I contend that of the 26 modern letters, at least 20 (and up to 23) can fit on the 7 seg display and still be recognizable. Granted the 7 seg alphabet would be forced to use the (currently) upper case form for some letters (like A), and the lower case form for others (like q), but at least one of the two forms fits the 7 segments for every letter except M,T,K,W,V,X. Since we already accept not having two forms for each letter, we may as well re-assign the former capital U as a "double sized u" aka W. As M is W upside down, the same trick applies to make a 7-seg M. Yes I've mangled the letters, but the outline of the shape is close enough that you won't trip up reading it in the context of a word. There's already some precedent for using "7" to replace T (as in 1337 5p34k). So that just leaves K,V,X as "not recognizable on 7 segment display".
But you've kind of made my point for me.
> and in keeping the letterforms sufficiently distinctive to quickly recognize whole words.
Just by evolution the letter forms evolve towards the minimal amount of distinguishable features needed to encode the whole alphabet. Evolution is an optimizer not a designer. The fact that there are still 3-5 letters left that didn't get optimized into 7 segments is what we should expect from such a process.