Running MongoDB effectively on AWS is very expensive. It's the opposite of what AWS is optimized for. It requires a dedicated amount of RAM that scales with your database, and it requires permanent storage that's about 100x the size of the actual data.
It's very much unlike a nice, bursty, CPU-bound web server.
Also, you can't use the big selling point of AWS, which is that you can scale it "elastically". Okay, you could, but it would be a terrible experience with lots of unavailability.