Or you can continue to improve your actual product while Stripe takes care of the rote billing issues. That's essentially Stripe's whole pitch, you could do everything they do on your own, but it's expensive and not central to your business.
Shameless plug here! We also created something we called our Smart Router engine at https://processout.com, which helps you connect to dozens of payment providers and optimize your transactions.
I also am confused. I've made sure that Stripe will not send any emails directly to my customers (disabling emails for successful payments, refunds) since I integrated with Stripe's webhooks for my own custom emails. Is there now some other option that I have to turn off for CC update emails?
(PM on Stripe Billing here) All emails from Stripe to customers (like credit card update emails to your customer, etc.) are off by default. This behavior is the same as all of our other emails to your customers: if you prefer to listen to webhooks & send your own, that's great!
so all the invoices I now see automatically created for all my pre-existing subscriptions, with their own Stripe-generated Invoice ID are NOT being sent out, are they?
How can I make sure of that? They have nothing to do with the actual invoices we already generate, send our customers, pass to our accountants and so forth and should any of these "Stripe-generated invoices" be made visibile to our customers it would create a HUGE accounting issue.