For most "practical" applications of first-class constraints, we do not see such complications: the quotient space of the restricted subspace by the f-flows (in other words, the orbit space) is well behaved enough to act as a differentiable manifold, which can be turned into a symplectic manifold by projecting the symplectic form of M onto it (this can be shown to be well defined). In light of the observation about physical observables mentioned earlier, we can work with this more "physical" smaller symplectic manifold, but with 2n fewer dimensions.