Knuth's argument looks compelling at first sight, but it is conditional on there needing to exist a single undisputed power function for all occasions, and I think this is simply false. When working with the binomial theorem, the meaning of exponentiation must certainly be taken to involve 00 being 1; but in other contexts this need not be the case, it can be undefined or zero or 42 or whatever the hell it likes, and we resolve the dispute with Knuth by pointing out that his exponentiation and ours aren't necessarily the same thing. Where it matters, make it clear.
Anybody who wants the binomial theorem (x + y)^n = sum_(k = 0)^n (n\choose k) x^k y^(n - k) to hold for at least one nonnegative integer n must believe that 0^0 = 1
is flawed of course: they might just be disappointed…
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