There’s a really good reason the lagging strand has to be done in such a weird backward fashion, rather than allowing DNA to be polymerized ‘in both directions’; its proofreading. As the polymerase moves along, it sometimes incorporates an incorrect base, and usually catches itself and removes the improperly paired base. It can then try again, and almost always adds the correct letter. (this in itself if insanely awesome.)

But a polymerase that evolved to elongate “backwards” wouldn’t have this proofreading option, because of the chemistry of the DNA backbone. Chew backwards from the growing end of a DNA strand, and you are always left with a reactive oxygen exposed to add the next base to. But from the other direction, if you chew away, you leave an unreactive phosphate group, to which no further bases can be added. So DNA can only grow in one direction!