Time reversal symmetry and quantum spin Hall effect

As it knows the edge states in QSHE are protected by TR symmetry, so any perturbation that are symmetric under time reversal cannot destroy these states. A key point is that for $T^{2}=-1$ we have a Kramers’ theorem, and indeed the edge states are Kramers pairs. But $T^{2}=-1$ only for system with an odd number of particles with half-integer spin, so it must be too hard to get experimentally QSHE system, because the number of electrons is too dirty quantity (our system is connected with leads). But indeed we have these systems in experiment and I don’t understand where am I wrong?