Our services are highly elastic, and can vary from processing 8 million events/day to 600 million events/day. Same as with our users, which are mainly active during work hours, with some running night shifts, and then fewer running weekends.
We are probably the prime-case for cloud, since elasticity is where you save cost by going away from dedicated hosting.
As for availability; our customers are highly dependant on us processing their data live, and them being able to monitor, get alarms and react on their data. They rely on us to notify whichever technician needs to fix their production line when it's stopped, since they loosing money for every minute the line is not running (true for almost any manufacturing company).
This means that we need a lot of redundancy, and these things are built-in to almost all AWS offerings.
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There's a case for dedicated servers still, I'll agree on that, but we are definitely benefiting from the cloud.