To implement the hardware based on ternary logic is much more complex and that is why binary won. It is much easier to process and store 2 representational states in each bit then 3. It is easier to tell if there is a charge or not vs determining the difference between a high charge, a medium charge, or no charge. It is easier to store and read information with 2 polarities vs 3 polarities.
Basically, a balanced-ternary system would be smaller and more efficient than a binary system that can match it. I'd like to see an open architecture chip designed and built with balanced ternary logic. It would probably need to be made from memristors once that is feasible. We will need a computing reboot at that time anyway in order to take full advantage of memristors.