Learn English – Should you hyphenate “high demand”

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 hyphen is . . . used in writing compound words which, without the hyphen, would be ambiguous, hard to read or overly long. Here, more than anywhere else in the whole field of punctuation, there is room for individual taste and judgement;

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.

Yes. It is not absolutely necessary, but I think this is one of the easier calls with hyphenation; adding clarity in combining the entire adjective into one unit, and matching quite a few dictionaries (most have it either as hyphenated or as both with hyphens predominant among the cited examples).