It's because the phone is a two-factor token that everyone has with them. With a secure processor being the hardware token and fingerprints or face scans biometrics. This makes it ideal for saving such sensitive data. I most frequently use it to digitally sign documents in a legally enforceable way.

The card you linked is similar, and a smart card was one of the previous versions of our system. The goal here was to make it universally accessible, and a smartphone is perfect for that.