It's easier because you only need to tap the app to verify. No need for OTP codes, though OTP is a fallback if your device is offline.
It's pretty easy to implement your own TOTP client if you don't like any of those. Here's a JS reference in 250 lines of code and HTML: https://code.google.com/p/google-authenticator/source/browse...
In MePIN's defense, DuoSecurity also has their own push notification for a single-tap login, so users are willing to trade interoperability for convenience.
I think anyone who would blindly use your proprietary two factor solution that makes it easier for end users to authorize other people to log in would be silly.
'No 2FA' is the real silly one here. Any 2FA is so much better than no 2FA, and usability has been a big issue so far in 2FA adoption.