Banks have never accepted browsers. They don't need to because they can require the web app be paired with a mobile app or SMS code to log in. Before they used mobile apps they issued smartcard readers (at least they did everywhere I lived). The smartcard readers were also used to digitally sign transactions.

In other words, there aren't many banks that let you take sensitive actions with just a browser and that's been true since the start of online banking.

These days they also apply differential risk analysis based on the device used to submit a transaction and do things to push people towards mobile. For instance in Switzerland there's now a whole standard for encoding invoices in QR codes. To pay those you must use the mobile apps.

Edit: people are getting hung up on the "never accepted browsers" part. It means they only use the browser for unimportant interactions. For important stuff like login or tx auth, they expect the use of separate hardware that's more controlled like a SIM card/mobile radio, smartcard or smartphone app. Yes some banks are more lax than others but in large parts of the world this was always true since the start of online banking.