I've been thinking a bit about some particular letter patterns that actually represent single entities. These include TH, QU, GH and probably OU/PH/NG – any others? That sets them a bit apart from the rest. Just a th-ou-gh-t... (the gh in that word is mostly silent now but used to be pronounced).
Incidentally, the reason we type TH and GH as letter pairs, from what I've been told, is that the Dutch type setters who first came to England in the late 15th Century to print the Bible and Arthur myth for William Caxton, didn't have lead type for the English Wynn (Ƿ/?) and Yogh (Ȝ) runes! Also, they got paid per letter so they certainly didn't mind making digraphs/bigrams out of the missing letters...
In Icelandic they still have þ/ð letters for unvoiced/voiced TH, and in some languages you can use a γ/ɣ or similar for GH. Ph/ph can be written as Φ/φ. By now, that won't happen in English of course! ლ( ʘ▽ʘ)ლ～?!
But maybe people who wish to improve their keystroke stats could take those on?! There isn't much chance of getting more keys on the keyboard, but with layers maybe it's an interesting thought – same number of strokes but the possibility of using home position and thumbs more. I'm thinking along the lines of mapping Th/th to AltGr+T/t etc.