Then, a while later, CBA pretty much phased out SMS-based 2FA (or they said that if you had the mobile app installed then you can no longer use it?). Only other supported option is in-app 2FA (no support for third-party TOTP apps). So I had to start opening the mobile app every time I needed a 2FA code. Then, within the last year or so, they made a new rule, that in order to log in to the web UI at all (just initial login, I'm not talking about sending money or any other high-risk action), you had to receive a push notification via the mobile app and tap "allow". So now I literally can't log in to the web UI without also logging in to the mobile app!
So, unfortunately, "just keep using the bank's website on desktop" is increasingly and deliberately becoming not an option. I assume there are many similar stories with other banks around the world.