It provides better density (for parity in manufacturing).
That they provide three states per 'bit' does not make them 'yes no maybe' any more than it means "true false file-not-found" - its an application level thing to decide how to interpret and label those three states, but they are not 'fuzzy' approximate states, they are absolute and exclusive.
Ternary components would actually be compatible with binary CPUs - the key distinction is if they are digital or analogue, not if they are binary, ternary or other based. Its a simple hardware problem to convert one base to another and provide interfaces in arbitrary bases - it won't require a new CPU architecture to have some memory that happened to be ternary, for example.