For a non-critical website or a web service, I can see AWS taking over for some or all parts.

For something handling financial transactions, or for anything of a high value, no.

I think there are a lot of sites out there that not having to administer their own machines is worth the minor loss of control. Sure, there will always be sites that need that control, but for many web apps (etc) out there, I think AWS will be worth the tradeoffs.