Local commutativity in QFT

Kallen, Some Aspects of the Formalism of Field Theory, in The Quantum Theory of Fields, Proceedings on the Twelfth Solvay Conference on Physics, 1961, p. 160:

local commutativity certainly should hold for macroscopic distances but… the assumption that it holds also for microscopic distances is an extrapolation for which there is no real logical foundation… we see that if we request local commutativity to hold exactly for space like distances larger than a certain length l, this means that we require the equality of our two analytic functions on the real axis to the left of a certain point on the negative real axis. This weaker assumption is enough to guarantee that the two analytic functions are equal everywhere and consequently that local commutativity holds also microscopically. Therefore, it is impossible to make a theory where one requires exact causality for macroscopic distances, has assumptions I and II fulfilled but tries to introduce a non-causal feature for small distances.