We've had a few queries for whether we could do this for SaaS companies paying via credit card too, as a Stripe integration. I'm still not sure if there is a real/big problem to be solved here that makes it worth entering.
Where we typically improve on whatever the accounting system has, is acting more like a CRM system for credit control. We typically have a lot more customisation and control over who gets chased with what message, we enable you to automatically send hard-copy payment demand letters. Also you can connect your accountant or bookkeeper to us (or rather they connect to your account) if they are doing credit control on your behalf.
Lastly we enable users to anonymously report when they get paid vs agreed terms to see if they are getting paid faster or slower than other suppliers.
On the email side, we've got a lot of optimizations and reporting baked into our service that most folks would find too difficult or time consuming to implement and maintain if they were doing this on their own. As a result, even folks who already had a standard "email customer when payment fails" webhooks implementation get much better results using Churn Buster. (For example, https://twitter.com/citadelgrad/status/499015554209185792 .) They also completely eliminate their administrative overhead and relating to failed payments. :-)
I hope you'll take us for a spin! Email me at andrew@churnbuster.io if you've got any questions or if you'd like to schedule a Skype call to talk about it.
I'm happy to freely share what I've learned, if anyone has questions about cutting churn and retaining SaaS customers. You can catch me on Twitter, where I'm @rfelix.