Recs.
Updated
Specs
Pros
Pro Closed Data
Banks hold a huge amount of data about you, which would be great for you to have easy access to. Most banks allow you to view some of this information through their sites after going through multiple checks to ensure you're you; but so far none that I know of have opened up an API to allow you to pull data into your app to grab complete sets of data, analyse your spending habits and thus better adjust them.
Pro Outdated Security Model: Spending Offline
Most cards have been upgraded to use Chip and Pin, which offers some level of security. However the old mechanism of signatures is still valid as a fallback option. Often people's signatures are inconsistent, making the need to forge them redundant and the process of checking them mere lip service security; and that's assuming the person's even bothered to sign their card.
Even when chip and pin is available and working, most people don't hide this 4 digit code, making it pretty easy for a supposed bystander to observe and remember.
Pro Outdated Security Model: Spending Online
Purchasing items online often still requires you to present your account details to the business you're purchasing from; which gives them all of the information they'd need to make purchases impersonating you.
An improved model would be to go somewhere you already have a trusted relationship (i.e. to your bank's site) and ask them to pay the vendor from your account; thus the supplier receives payment without any way to reuse the information supplied.