I grew up in an era where running your own servers was just generally accepted practice. It's been fascinating watching how dramatically that viewpoint has shifted over the years to the point where it is now a novel idea to do so.
I wonder how much of this is just the industry maturing/specialising. We don't think it's weird that most people don't mill their own flour when they bake bread, so long as the quality of the flour is good enough we're happy for someone else to do it for us.
In the same way most people/companies don't really need to care what hardware their application runs on, only that it meets some bar of quality/cost that's appropriate for them. If someone else is delivering this then you've removed a small department's worth of overhead/planning from your corporate structure.