In particular, it doesn't scale well at all with the number of choices (the familiar curse of dimensionality). You can reasonably test two variants, but if your design could plausibly vary along, say, 10 axes (not uncommon), you're going to have trouble collecting sufficient data to cover the whole 10-dimensional theoretical design space. So data-driven design can usually only be applied to a small part of the design space, typically testing a small number of alternatives.