Note I'm not including their networking costs to get to the last mile, where they place a lot of their own boxes in ISP facilities pretty close to users, that would be about the same however they were doing core IT.
IME cloud _can_ easily be more expensive and more work than bare metal, in house or colocated. If course it depends upon the workload and the tools/resources available to manage it. Even with clouds there is still server management to do.
More work - definitely not. No matter how hard managing your AWS workflows is, bare metal will always be all that same work plus everything else related to hardware, cooling, power management, ISP and more.
Sure you have "hardware, cooling, power management, ISP and more", but that's all easy, especially compared to managing AWS workflows.