16core processor along may cost around 1000 - 2000$ approx. or more depending on quality. One advantage of AWS like cloud provider is that you get flexibility in scaling you application, basic level security and are time tested. Also, most of the server infrastructure is managed by AWS along user on need to worry about maintaining there application, security setup. To maintain a physical server the cost of server is just one among many expense. You need to have reliable security and maintenance to make it which wont be any cheap than 600$or 1000$ per month.
AWS have different premium and support plans based on which offer could varying,
This was just a thought as there were lot of people encouraging to share thoughts on game improvement as the team wasnt much during initial release. This was two year old question which even i had forgot as not much response came earlier, no offense. I myself is working as cloud application developer for 5 years, hence the idea.
A lot of companies are moving there on premise(physical) server to cloud in order to reduce cost. Netflix is one example. Please refer link: https://aws.amazon.com/solutions/case-studies/netflix-kinesis-data-streams/#:~:text=Netflix%20uses%20Amazon%20Web%20Services,100%2C000%20server%20instances%20on%20AWS.
https://aws.amazon.com/