This comes from LaRussa being a tool. His black book says that young lefties cannot possibly improve against lefthanded pitchers, therefore they shouldn't be allowed to try (see: Drew, J.D.)
Wilson and Taguchi have no business making the Royals, let alone a team with playoff aspirations.
In a few weeks, Taguchi and Wilson will be exposed as completely worthless and LaRussa will have no choice but to start Duncan against lefties. Encarnacion will be back soon enough to provide a decent RH bat (against lefties, he sucks against righties), that could free LaRussa up to take a chance by putting Duncan in. Or at least that will be his rationale, nobody could possibly suck any more than Preston Wilson....except for So Taguchi.
Duncan will get his ABs in due time.