The more I think about it, the less sure I am. Experience will probably have to be the judge.
I suspect it IS slowing down your trashing a little on the whole. In exchange you quickly get an extra shot at your new Silver, but not really the most impressive odds of hitting $5 (7/18, by my math). And even if the latter is good, are you going to prioritize an early buy over trashing speed? Maybe sometimes, but this preference seems perhaps a little incongruous with opening Doctor in the first place.