People use it because they
think they need the scalability. The reality is that almost nobody that use EC2 have the ability to scale up or down that quickly, and even fewer needs it:
Most sites have a fairly stable base load, and most dedicated providers these day can provision in less than 24 hours, so you at most need the ability to handle short spikes or growth over hours rather than days.
And EC2 is expensive enough that you can handle huge variations by buying extra dedicated capacity to cope. But the (far) cheaper option still is to handle your base load on a cheaper provider, and build your system to be able to scale using EC2 or another cloud provider to handle spikes.
WIth more and more providers providing "hybrid" services with colocation, dedicated, dedicated vms (single vm per physical server), and cloud servers all (or most) on offer from one location, this gets even easier - you can sometimes even get virtual private lans across dedicated and cloud servers without having to mess with your own vpn or pay for the bandwidth