I won't travel to another city or country just to hand money in cash.
I won't travel to a branch to... I have never ever written or received a cheque, what the heck even is a cheque? A piece of paper someone can photo-copy?
I used to be able to do all of my banking from a web browser, from any browser/OS I liked. I've had a fob that displayed a 6-digit code rotating every 30s. This used to be simple and secure. What you propose is ludditism.
You are also quite quick to dismiss cheques as someone that never even tried them...
Online banking is dead simple to secure: require a TOTP token. It's something you have (like a debit card) + something you know (PIN/password). The poison being introduced is through a third party, and entirely unrelated to the original function.