On a related note, the finance-related apps on my phone all offer me the option to sign in with a fingerprint sensor. Arguably you have two forms of authentication there: the presence of the physical device itself (using the secure element or whatever it is), as well as the biometric identifier (fingerprint scanner).
Neither of those are present when logging into your bank from its website, and I would also suspect that jailbreaking a phone significantly reduces the trust you can have in either.
Also, from a bank's perspective, all they care about is reducing their liability, without inconveniencing too many customers. In that context, it makes a lot of sense for banks to disallow their products from being used on jailbroken phones.
Neither of those are present when logging into your bank from its website, and I would also suspect that jailbreaking a phone significantly reduces the trust you can have in either.
Also, from a bank's perspective, all they care about is reducing their liability, without inconveniencing too many customers. In that context, it makes a lot of sense for banks to disallow their products from being used on jailbroken phones.