Why did you decide to write the GNU Affero GPLv3 as a separate license?
Early drafts of GPLv3 allowed licensors to add an Affero-like requirement to publish source in section 7. However, some companies that develop and rely upon free software consider this requirement to be too burdensome. They want to avoid code with this requirement, and expressed concern about the administrative costs of checking code for this additional requirement. By publishing the GNU Affero GPLv3 as a separate license, with provisions in it and GPLv3 to allow code under these licenses to link to each other, we accomplish all of our original goals while making it easier to determine which code has the source publication requirement.