Delete / remove birthday calendar? (or at least stop reminders?)

I think I must be missing something very obvious, but how do I delete or remove the birthday calendar that is built in to iOS? I already stopped it from showing when I go into the Calendar app in iOS (Calendars -> uncheck Birthdays). But the notifications still show up from that calendar even though that calendar isn't showing. And there isn't a way (that I've been able to find) to delete the calendar.

And before anyone asks, yes, there are some birthdays that I want to keep in the contact's details but not necessarily get reminders on.

If there is no way to remove the birthday calendar, which seems completely inane, since I don't know why we wouldn't be given the option of removing that, can we at least stop reminders from that calendar?