I'd also add that while we can signify binary with high and low voltages the same doesn't work as well for trinary as you would need a mid voltage.

One likley issue here is that while it may seem like electrical states change instantly they actualy take a tiny amount of time as voltage drains from a high representing a 1 to a low representing a 0. Now add a mid voltage between 1 and 0 and the voltage has to actualy pass this mid state on its way from a 1 to a 0 meaning that if you read the systems state at the wrong time you could easily mistake a voltage in transition for one that's intended to be this mid voltage. . This is actualy a common issue with overclocking as the clock rate outruns the ability for the voltage states to change, however in the case of a binary system it's possible to stabilize the system again with a bit of overvolting at the expense of producing more heat.

So unfortunately, using our traditional system of representing two states becomes a lot less stable when adding a third state, and making a stable system that can represent trinary would likely add a lot of complexity.