I agree with you I like Chebyshev Distance too, but as far I can tell you, dot product is not that much more complex than Chebyshev, I'd classify them as about the same. But if there is a good argument to argue Chebyshev is much simpler, and it's about as good, then I'd prefer Chebyshev too.

Having said this, nowadays the metric I like the most is SAD (sum of absolute difference) which is Sum(abs(x2i - x1i)), which is the L1-norm of the difference image. I find this oddly easy/simple to reason and implement, so I use it in any model where it works.