The real reason why people use AWS is because it's convenient.
In the last year I've noticed AWS is finally catching my eye on price, and I'm a big co-lo self-managed fan due to the cost savings. In a few more years I could see myself switching everything over and not feeling bad about the cost.
In that time Amazon's value proposition will chase down toward where Linode and Digital Ocean are at today. Let's say their system power (the sum of the hardware) will go up by 50% every year, while their prices fall 25% every year per 2014 defined unit of power. Even though I consider Amazon expensive today, it won't be long at this point before they start to outstrip my scale of service demand (I'll never be operating Twitter or Foursquare on AWS).
If you're trying to start a business in India or Egypt, you're VASTLY better off outsourcing your IT to a dependable third party like AWS -- particularly as those costs drop over the next decade through economies of scale and technological progress. I'm sure the eventual goal is to sell AWS and its competitors as replacements for virtually all business IT and even personal computers -- even in stable Western countries. Current prices may have finally started to be competitive with local hosting, but we haven't even touched the potential of cloud computing yet.
For most companies out there, that involves hiring someone with Linux/Windows server management skills. Even in an engineering company, if you have a choice between spending engineer's time on engineering projects or system management, the company usually gets more bang for the buck for the former.
Put differently, the best backend developers are also the ones that can compile nginx from source (a rare talent nowadays apparently) and have it running reliably within the hour. Better by no small factor either. There's no shortage of them.
A few years back you could have the same argument with an army of Exchange administrators who would point out how ridiculous it would be to trust your entire company's email infrastructure to Gmail, yet here we are.
You do need things like build-essential installed (which we'd let them install however they wanted). And a blank ./configure normally complains about missing pcre and maybe gzip (I forget). But we'd just tell them they could install without it (and the error message makes it very clear how to do that (--without-pcre or whatever).
Very sad.
What IaaS really saves you is the tedium of dealing with the physical aspects of servers. No requisitioning hardware, driving to co-los, dealing with phasing hardware out, etc.
if your definition of cheaper is having to cough up the large upfront capital to rent/buy a place, rent/buy a rack(s), and then pay somebody (or DIY) to install, hook up power and test disaster recovery options etc...then yes, it's cheaper.
The amount of dedicated hardware you can rent for $1,000 per month is several times beyond what you can get from Amazon for the same price. And if you have a demand for lots of bandwidth, Amazon will cost more just on bandwidth than for the entire dedicated setup somewhere else.
Amazon will drill you for $1,000+ for just 10tb of bandwidth alone. Today 10tb of bandwidth on a 1gbps line is almost the assumed base you get with a $100-$150 dedicated box.