The problem has more to do with the mechanics of plurality voting than presidential vs parliamentary systems. Parliamentary systems can and are subject to the

The problem has more to do with the mechanics of plurality voting than presidential vs parliamentary systems. Parliamentary systems can and are subject to the same winner take all mechanics. The scenario you outline would best be remedied via a ranked voting method such as IRV or approval voting. The one thing I would incorporate from some parliamentary systems into the US system is proportional representation. PR + IRV = more equitable representation of non-gamified votes.