AWS specifically might not, but I can say with some certainty that cloud providers can host AGPL software. It's not impossible that Compose (the now IBM-owned cloud database hosting company) pulled in more revenue from RethinkDB than RethinkDB, Inc., did.
Yeah, it's a matter of risk. Rightly or wrongly you could get hit with a lawsuit that says "we have infected your entire control plane; open-source it or die" and every cloud provider has to weigh that for themselves.
