You can get those same "deep storage" tiers on prem for a fraction of the cost of AWS. There's no scenario, short you of you running the systems at less than 40% capacity, that AWS is cheaper. You have to be criminally inefficient or very very very small (like less than one server small) for AWS to EVER be a cost play.
I should add, bursty workloads like batch processing can be a cost play simply because a once-a-month even that is time sensitive can benefit greatly from instant* CPU that you don't have to pay for the rest of the month. Those workloads tend to be very niche and one-off for most businesses though.
I don't know a lot about the huge scale side, but I tried running a teeny little server of my own on AWS, and it's way overpriced and over-complicated. You can get a single server for like 20% of the price on any number of hosting services. Digital Ocean works pretty well for me right now.
AWS is somewhat lucky in that its best market was primarily organizations where an offering like it was actually very simple and transparent is what is desired and that price / performance is not what it competes well upon. This is rather different from their main business that's very focused upon lowering costs and merely by being online is in its own way performance.
Internal IT in enterprise is so unbelievably terrible in the Fortune 500 that even the worst mass shared hosting provider probably offers more compelling value. Amazon didn't have much of a bar to cross in technicals as much as in value proposition to encourage a transition worth future benefits.
I should add, bursty workloads like batch processing can be a cost play simply because a once-a-month even that is time sensitive can benefit greatly from instant* CPU that you don't have to pay for the rest of the month. Those workloads tend to be very niche and one-off for most businesses though.