As mentioned in section 3.5, the mere requirement for the Floer theoretic obstruction criterion (i.e. the stability condition) to make sense for Lagrangian currents is already very constraining. Most statements are simply impossible to make without concepts that need at least $C^{1}$-regularity, and the bordism currents between integration cycles are among the rare exceptions. This was one of the heuristic arguments in section 3.5 that obstructions must come from bordism currents.