Earlier quoted context omitted.
Well, this assumes that it won't be compromised during an Internet banking session. Since I have a workaround (use the mobile app for personal banking, go to the bank for business stuff - which I don't need to do often) it doesn't seem worth the trouble and risk.
How would it be compromised if you only connect to the bank?
The bank requires their own ActiveX control and external software which the ActiveX control communicates with, both of questionable quality. Surely that's one of the more likely attack vectors you could have on a system?