This is hardly some sort of unique New Yorker idiosynchrasy. Rather, it’s merely an older tradition.
Writing Zoë, Noël, reëlect, coöperate, zoölogical, mosaïc, aïoli, cacoëpistic, hyperoödon, haliæëtos, naïve, Moët, naïveté, Thaïs, monoïdeism, panzoöty, Laocoön, langue d’oïl, Boötes, faröelite, caïque, &c is actually an older orthographic style.
This style fell into disuse as people subjected to the infinite tyranny of typewriters (and their ASCII derivatives) bereft of proper diacritics got out of the habit of using things they didn’t know how to type. I rather hate seeing *Zoe written by people who are too lazy to write Zoë properly.
On the other hand, English has never used a diaeresis in words like coalesce, where one might expect *coälesce to differentiate from something related to coal. Similarly, we’ve never used *reäct for react. There is also the tendency to drop hyphens and diacritics from assimilated words. Notice it’s just zoology in modern writing, not the original zoölogy, and you almost always see dichroic and dichroous instead of dichroïc and dichroöus.
I’d sometimes rather see a diaeresis than a hyphen myself if it comes to that. I actually prefer writing coöccurrence, coössify, demosaïcking, reënact, reïnvent (not a rein-vent, whatever that might be), reëxamine, intraätomic, pal(a)eoöceanography, proöxidant, &c to make it clear what’s afoot, where others might use a hyphen or nothing at all. I’m trying to be considerate for the reader, and consistent.
And yes, coopering is a real word, one with three syllables, though, not four. Hence the preference of writing coöperate to show that it has four syllables instead of just three, and is unrelated to coopers.
J.R.R. Tolkien, a very careful writer of English from a slightly earlier era than our own, uses the diaeresis a fair bit in his writings. Consider the raven Röac from The Hobbit; its name is meant to be bisyllabic onomatopoeia for its croaking cry (or is that croäking? :). Or namarië, Eärendel, or Manwë; written using Tolkien’s own phonetic tengwar script, these need no markings to indicate those vowels should be pronounced, but as an aid to English-speaking readers using the Latin script and used to “silent” letters, it helps to mark these explicitly.
By the way, the word diaeresis is so spelled in the Unicode Standard. You will find older books that spell it diæresis, which uses yet another non-typewriter letter. And it is not uncommon to find it spelled dieresis in American writing.
Best Answer
The hyphen is not required in the first pair. As you say, high is simply an adjective and performance is simply a noun which high modifies.
In the second pair, high is again an adjective and performance is a noun functioning as an adjective and together they modify computing. The question to ask is whether the absence of a hyphen between high and performance creates ambiguity. Is it possible that a reader might somehow think that computing is modified independently by both high and performance? Probably not. Nevertheless, as the late R L Trask wrote in ‘The Penguin Guide to Punctuation’:
The absence of a hyphen might cause the reader a brief moment’s uncertainty over whether high and computing are to be taken separately or as a whole. If you think that might make the piece ‘hard to read’, then you would be well advised to use the hyphen.