I have to take a stand against the expression which have become so popular:
"The cloud is just someone else's computer."
First off; it might be...
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Still basically "someone else's computer" in the end, no matter how it's managed.
It's a statement about the fact that the data you put in the "cloud" isn't stored in a magic secure place but in someone else's hard drive.
It doesn't excludes the fact that it has to be managed and that it's a lot of work.
Sometimes it feels like people mean "oh, it's just a computer running somewhere else", but it's also so much more around it.
But I see your point. "The cloud" isn't a magical place where code goes to live and make things happen.
For me it was always "someone else's computer" and not "someone else's computer". Privacy goes first and here you entrust your data to other people, not just upload it "to the Internet".
Whenever I use this phrase it's because my company has its own cloud and it isn't beneficial for us to run our software on another company's cloud.
It might benefit in some case though, right? Could there be a service operated by some provider more tailored to a use-case or backed by some expertise you don't have in house?
Yeah I forgot about video streaming. We don't want that throughput on our lines. So not just someone else's computer, but their ISP too.
As far as hosting vs. support... I can't think of an example where we haven't chosen on-prem (if available) and, if the software is exotic, then hired contracted development/support.