Will never happen
Nobody is going to run 3-logic computers. Not now, not in a 1000 years.
Even if some development makes 3-logic hardware attractive, it would be WAY WAY easier to just ignore and remove the 3rd state then to deal with 3-logic.
By the time someone comes up with a good 3-logic design, there will be a faster 2-logic machine, making 3-logic forever obsolete.
4-logic or 8-logic might be nice though.....