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This probably makes for a thoroughly unsatisfying answer, but there's probably far stronger *cultural* pressure than technical pressure.  In European-derived cultures, we mostly group numbers by powers of one thousand as you suggest, and anybody doing something else should either have an extremely good reason ("it actually represents a series of decimal values, but we store them together, because we learned programming in 1967") or would get laughed out of any code review.

However, people in East Asian cultures group digits as factors of *ten* thousand in speech, even though they'll (usually) write it following European conventions.  And India generally does pairwise separation, except for the final three digits.  I assume that other approaches exist, but those get commonly cited.

So, while in power-of-two bases, it's probably safe to assume that some natural word-multiple boundary (eight in binary, three in octal, and four in hexadecimal seems consistent in what I've seen over the years, but as another answer points out, architecture may easily figure in, here) could and should become a strongly-encouraged convention, we'd want to take care that a convention for decimal representation doesn't ask billions of people to write code that's less readable for them.