If you go over the limit they ask you to confirm in a way that requires the phone anyway
Oh interesting. Where I am if you go over the limit (usually $100), you just have to input your PIN. But $100 is enough to get up to some serious trouble, considering it's a per-purchase limit.
And I've both never heard of banks using the NFC directly (as opposed to using Google, Apple, Garmin etc. Pay), and wouldn't trust them in the slightest with it even if they did offer it, because they're not exactly known for great security. (And I'll take security over privacy any day.)