That is exactly the analogy I have a problem with, it is variously explained with cars in parking lots, people on seats, .... It is wrong however, the electrons

That is exactly the analogy I have a problem with, it is variously explained with cars in parking lots, people on seats, .... It is wrong however, the electrons do not move one at a time, they move in unison opposite to the normal flow of current. Apart from theoretical considerations, we know it has to be like this because the voltage induced by the Hall effect flips for these kinds of semiconductors, and since there are no positively charged free particles in solids, this has to mean the electrons are now moving in the other direction, giving a complete illusion of a positive charge carrier.