Free, open-source software is about control: controlling what code manipulates your data.
In short, it seems that the license really doesn't really do much of substance for the user, and just saddles the operator with extra burdens.
But it obliges you to provide or make available those changes if the use will "propogate" the work.
By the way, the AGPL3 definition of "propagate" looks exactly the same as that of the the regular GPL3. Operating software as a server doesn't fall under "propagate".
For self-service, this means that you're not locked out of the development capabilities of the service you've left -- though that arguably creates a free-rider problem for that service.
* You know what code is providing your services.
* You have the option to run that code yourself.
* Other service providers can provide the same service using the same code, so you're not locked in.
1. I've long heard that various SaaS companies really didn't like the Affero General Public License. Kuhn makes a case for why this is a validly justified concern, something I'd not previously considered.
2. The copyleft restriction termination is a really interesting concept, though not without its own set of consequences which should be closely examined. Historically, the advantage of copyleft has been that it applies equally to all. The abuse of it (by firms also marketing properietary solutions) is a problem, but removing copyleft obligations entirely might not go as intended.
3. Copyright assignments to copylefted codebases without an explicit restriction of those to require copyleft-only usage, a distinction which differentiates strongly between the uses at, say, FSF vs. MySQL AG / Oracle, clearly also present issues, as has long been argued.