In QFT, as I read, it appears naturally. It is connected with Poincare algebra, doesn't it?
As explanation of the main part of the question.
Operator of relativistic orbital angular momentum 4-tensor and 4-impulse operator creates Poincare algebra. It follows that eigenvalues of vector of angular momentum operator are expressed through the whole or half-integer values (in $\hbar $ units). But using only orbital momentum operator causes the possibility of having only integer values. We can artificially add operator, which implements an irreducible representation, so it doesn't connected with coordinate representation and may have half-integer values. But this method is an artificial, because without experimantal proof of existing of spin we can easily operate only with orbital angular momentum. In contrast, in quantum field theory, the spin occurs more naturally (?).