If you really want to implement a decline feature you could make it so you can either override with the app, or it wont decline the 2nd time you attempt a payment with the same retailer, or wont decline another payment for X minutes based on hard targets. This would require more backend at the payment end though (probably best to have payment management system as separate as possible from the app as possible), and it might annoy retailers. As a primary card you have to be able to make a payment in certain situations in person, for example a restaurant where you’ve just eaten, so I think flat denying payment/requiring app use isn’t viable.
An interesting opportunity crops up more with online retailers, where you don’t have the embarrassment of a card not working/there isn’t a risk you already have the product/service (i.e. you don’t absolutely need to make a payment).
When you use a card to pay online it appears the card has a chance to authenticate with the user. My Lloyds card just brings up a spinning circle (clicksafe or something like that) and does nothing, but I assume at this point you could request payment authorisation at the app, and because it’s online payment there is a lot less pressure, and they’re likely to have internet access. So why would this be good? Firstly this could be used when you’re going to go over a target, whilst allowing an easy override, for example you might be going over your shopping target but you’re actually using amazon pantry, so it’s really food, or you might be buying a gift you don’t want to count to a target, or you might just accept you’re going over.
I can see it having a second use though, targeting addictive/compulsive spending. Let’s say you’re a bit of a gambling addict, I don’t know how much you’d spend, but let’s say you’ve allowed yourself £100 a week and have used it all. When you try to pay a company known to be gambling online, during the authorisation stage the app could request authorisation of the transaction, showing you how much of the target you’re spent, and optionally a personalised message written by the user for motivation. The same system could be used to target online compulsive spending, and I think it would work well in an online shopping environment when you aren’t under pressure for a card to immediately go through. The user still has complete control over their transaction, but is presented with a choice. You give them a moment to think and reconsider their choice, and let them emotionally blackmail themselves into doing what they want to long term.
You would have to consider the use case where a user is making a payment without the app to hand, but you could apply the 2nd attempt system mentioned above as one solution to that.