When I worked in Sony games I had the choice between AWS and the IT department. The IT department was fine, just it was a 6 month lead time for the hardware and they had a tendency to optimize servers they didn't understand.
The problem was that they wanted 6 months and a capacity plan. 2 months to get me a test server. I knew server capacity about 2 weeks before launch. I also needed 5 server class machines with which to test against (which was the end cluster number) and the kicker which was 250 load generators to prove it.
The real kicker is that for many games load peak is the Friday after launch, we really only needed 1 machine a week later, and .25 going forward thereafter.
With the IT department we would have bought $160k worth of servers. And we still couldn't have actually tested things without AWS. AWS Cost $30k the first year and then we actually moved to new instance classes which cost $12k, $6k, and $1k a year thereafter. It was enough cost dropping that it wasn't worth dev time to even downgrade the cluster to a single instance.
None of that includes what IT would have cost to run the hardware. I'd make the same choice every time.