Exactly plus at scale AWS doesn't do everything either, a sysadmin or at least consultants are still needed to navigate the gotchas and help with how to better provision the stack. AWS instances don't just scale themselves.
There is one specific case when I recommend AWS instead of dedicated servers and it's for customers who have widely varying traffic with predictable peaks. In that case having the flexibility afforded by cloud providers to increase the number of instances temporarily to deal with the peak makes sense.
The only good use-case I know for AWS and it's ilk is if you need a 10,000 node cluster for a few hours to do some heavily compute intensive work which does not require a very large amount of data to be imported and exported afterwards. This is a pretty limited number of use cases but for those situations it absolutely rocks. Anything else I'd run the numbers very carefully.
I don't think that is correct. There are thousands of startups on AWS (an IAAS cloud) that don't run 10K node clusters. While they cost may be high, it is pay as you go. I have a rack full of computers at home and I still have some things served by AWS. The PAAS model (e.g. Heroku, Bluemix) is becoming popular today but those are often hosted in IAAS clouds.
There is one specific case when I recommend AWS instead of dedicated servers and it's for customers who have widely varying traffic with predictable peaks. In that case having the flexibility afforded by cloud providers to increase the number of instances temporarily to deal with the peak makes sense.