Your point that only the high-quality works survive is also wrong, as I tried to explain. We know of plays that existed but have not survived but would most likely have been pretty good, to judge by the writers (The Isle of Dogs by Ben Jonson and Thomas Nashe, for instance, which was suppressed by the censor). And some of those that did survive are just not very good. Survival of a work of literature, the further back you go, depends on a lot of other factors than quality.

It's really circular logic to say that it was good because it survived and that it survived because it was good.

I would expect someone who is a writer or has studied English literature to some degree to know at least two from the list (Marlowe and Jonson), and some plays like The Shoemaker's Holiday (by Dekker) and The Knight of the Burning Pestle (by Beaumont) are popular with amateur acting groups, so you can't really say that it's only Shakespeare.