Indeed, this captures some sense in which the truth of T requires that there be Ks among the values of the variables. For example, any interpretation that makes ‘∃x Unicorn(x)’ true will have some entity in its domain also be in the extension of ‘Unicorn’. This entity needn't be a unicorn, of course. But that's all to the good. It is the price one pays, the non-believer in unicorns might say, if one wants to be able to say that a theory is ontologically committed to unicorns.  But note that the notion of ontological commitment is now entirely formal. Because interpretations are generalized over, the actual interpretation of ‘K’ plays no role. Ontological commitment is essentially intra-linguistic, rather than a relation between language and the world. 