Isn't it my job as a Stripe Customer to build that functionality into my own app so that I can manage it in the way that works best for my customers?
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.
"Email invoice to customer when it is created"
was on by default but it appears only for "Invoices sent to customer for manual payment"