All my bank accounts are tied up to my phone. They're phone dependent rather than SIM-dependent though.
The only time my accounts will get compromised is if my phone gets stolen, and they figure out my passwords.
Phishing sites are a great risk for those who do online banking through their laptops. But with a phone app, it's quite difficult to mistake the real banking app from a fake one.
As with any new technology, there are always risks. But with the extreme convenience of online banking apps, I can't imagine going back to the olden days where I had to go to a bank just to transfer money to another account, or invest more funds into UITFs, or transfer money to my stocks account.