Why would I want to stop them making it available as a network service except as a way of circumventing the copyleft by effectively distributing it without actually distributing it (which AIUI the AGPL fixes)? If you want to place restrictions on how people are allowed to use the software then A) I don't see the relevance of AWS as a special case, and B) go ahead but don't imply the "open source crowd" are being unreasonable by not considering it open source.
You'd want to stop them if like in TFA you don't actually want to provide open source software but rather want to sell your software as a service with free marketing from being "open source".