A train or bus that only carries a few people is not really a problem. Because labor costs are the majority of public transit operating costs not vehicles it makes sense to use the largest vehicle everywhere. Using minibuses or smaller train cars just means you get capacity issues during rush hour and you can't standardize on one vehicle.

You are right that public transit does not go door to door. Riders are expected to walk a block to the nearest station. If a transit system tries to replicate taxi service it would be too expensive or would really inflate waiting times for a ride.