Does AWS or any other large cloud provider offer this type of service?
Doesn't AWS charge an arm and a leg for traffic?
Maybe you could run www on AWS and your real service somewhere with reasonable prices for traffic. In my experience, people who randomly DDoS tend to hit www rather than useful parts of a service.
I don't believe I've been charged for this type of attack. The one you should look out for if you are new to AWS and trying to do this "trick" is L7 repeated downloads of high-file-size content to consume your budget rapidly.
How an one protect against this type of attack?
GCP Network has built in DoS mitigation as well (e.g. in the load balancing layer) so you get some protection from that for free.