A key for "TH" has been suggested here before, but I doubt it would work in practice.  We are so used to typing letters (graphemes), not sounds (phonemes).  How long would it take you to adjust to typing "the" as th-e instead of t-h-e?  Or is that because I'm not a native English speaker?  In my language Dutch, "ij" is sometimes considered a single letter, and hand-written as ÿ, but I would never type it that way.

Another issue would be capitalisation; should Shift+"th" produce "TH" or "Th"?  You don't want to depend on auto correct?

For comparison; Serbian is a bi-alphabetical language (Latin and Cyrillic both in use today), the Latin alphabet has digrahs lj, nj, dž that are single Cyrillic characters љ, њ, џ, and are collated as single characters in both alphabets, but their Latin keyboard (QWERTZ) has no digraph keys.  (The corresponding keys instead have Q, W, X, which are not used in the language and have no Cyrillic counterpart.)

Yeah, I don't think it seems too tempting for me but we had a chat at the Discord and it got me thinking.

I'd think that Shift+T would produce Th because that's what you'd use in normal text. I had the same problem with my dead key table entries for the ligatures ij/IJ, lj/Lj/LJ, nj/Nj/NJ, dz/Dz/DZ and dž/Dž/DŽ; I resorted to using the AltGr mappings for the relevant keys to release the all-cap versions (so, e.g., l→lj, L→Lj and ł→LJ). It's a hack since it's only on my eD layout the AltGr mapped glyphs are connected to their base letters.

I don’t think putting those digraphs on the AltGr layer is a good idea. It’s surely only somewhat working when your right thumb is agile enough, your space bar is short and/or you are using a wide mod. But even then it’s probably a waste of space. At least G, H, N, O, T and U should be in comfortable positions anyway and  bigrams of those letters should be easy to type.

Still, I think there is some value to the idea of giving entities like that more attention when designing a keyboard layout than their bare bigram frequency would suggest. I certainly did that when placing P (I’m not using Colemak). I chose a layout that fared slightly worse in my calculations, because it did feel better. The difference probably lay in the SP, PH and also PF bigrams, which can be entities in German and/or English.

Generally, I’d rather reduce the number of keys needed to write text. I actually got rid of the keys for Ä, Ö, Ü and ß. Instead my ISO key is now a multi-purpose dead key (◌) that allows me to comfortably write these letters (and more) as if they were simple bigrams (◌A etc.). But that may be just me, I just like nice bigrams. Certainly more so than holding down modifier keys. My shift keys are sticky, so uppercase letters also have that simple bigram feel.

I also don't think it'd be worth it for the majority of typers. It was just a discussion at the Discord that got me thinking. The leap from a letter-by-letter layout to proper stenography which is hella fast but a nightmare to learn from what I gather, is overmuch for most non-professional typists. So maybe some ambitious souls could map some n-grams and save some effort...?

But for bigrams the answer is pretty much a given I guess: You'd need two strokes or an overlong stretch to save two strokes and that amounts to a zero sum game – unless you can benefit substantially from an ergonomic advantage of the first stroke (the modifier or dead key). Possibly, the bracket keys which are often used for locale letters like æøåüéèñ etc, might hold TH and another digraph... which would make them pinky stretches but with the Wide mod they'd be half-long index stretches instead so maybe? That'd of course only appeal to staunch text typists who don't use brackets as much.

Or, could the answer be to look towards the most used n>2-grams? Typing THE/AND/ING with two strokes each sounds just a bit nice, and those may be common enough for the dedicated soul to care about. But after those, the tri+gram frequencies drop off rather sharply.

Well. I don't know. I don't think this is the sort of thing I personally would do unless I were convinced of a substantial benefit which I am not. For one, it makes you even more dependent on your typing software and I'm already too dependent on it...   ￣(=⌒ᆺ⌒=)￣