I guess the biggest downside is the speed of scaling that they can do. As it is limited by how fast they can purchase and install new storage device. But with the use case of Internet Archive, that shouldn't matter much.
Also, bare-metal doesn't necessarily mean owning the hardware. You can rent it too. There are providers that provide bare-metal in one-click and sometimes available within minutes.
It really depends on what scale you're talking about. When you're a startup and suddenly land on the front page of HN, you might need 100x or 1000x your current capacity - in which case AWS will be useful to no end.
If, on the other hand, you're an established name with quite a bit of traffic already and the maximum uptick you will reasonably experience is 2x-3x, the argument holds far less water.