  A large amount of effort has recently been put into understanding the barren
plateau phenomenon. In this perspective article, we face the increasingly loud
elephant in the room and ask a question that has been hinted at by many but not
explicitly addressed: Can the structure that allows one to avoid barren
plateaus also be leveraged to efficiently simulate the loss classically? We
present strong evidence that commonly used models with provable absence of
barren plateaus are also classically simulable, provided that one can collect
some classical data from quantum devices during an initial data acquisition
phase. This follows from the observation that barren plateaus result from a
curse of dimensionality, and that current approaches for solving them end up
encoding the problem into some small, classically simulable, subspaces. Thus,
while stressing quantum computers can be essential for collecting data, our
analysis sheds serious doubt on the non-classicality of the information
processing capabilities of parametrized quantum circuits for barren
plateau-free landscapes. We end by discussing caveats in our arguments, the
role of smart initializations and the possibility of provably superpolynomial,
or simply practical, advantages from running parametrized quantum circuits.
