SMS is not a secure messaging channel. All it takes is for a rogue employee of the telecom (or an SMS gateway used) to sniff traffic to know which numbers have what balances, and then one day create spoofed SMS messages to transfer those balances.

There was an SMS-based mobile will that was developed for BCash, called CoinText. It is now defunct. And yes, losses for some users due to spoofed messages was occurring before they shut down the service.

How mobile banking and mobile money networks operate is on a smartphone app, or using either USSD or STK (SIM Toolkit). STK can run on "feature phones" which feature a JVM (which nearly all feature phones made in the past 20 years support). But STK requires a certificate from the telecom operator, so a third party couldn't offer such a wallet without working with (i.e., paying fees to) the mobile network telecom operator. It's possible with bitcoin being a "benchmark" currency in the country that a mobile money operator (e.g., Orange Money, which currently operates in CAR) would add a bitcoin wallet to their service. That would definitely be a global first!!