This is obviously wrong. It's possible to do the same banking things using the bank's website both from general purpose PCs and browsers on phones for which jailbreak detection is not possible in the browser.
Jailbreak detection is done by testing for the presence of common things that allow the device owner to control the device. The device owner controlling the device is not a problem for banking. Meanwhile a malicious third party wouldn't inherently need to make use of any of those and would have strong incentives to avoid using any that trigger jailbreak detection, so it's no help there either.
And for the same reason it's basically useless for detecting cheating. Because if you jailbreak your phone so you can install some apps from outside the store and then it breaks your games, you might grumble and decide you want to play the game more. But if you jailbreak your phone because you want to cheat at games, your next step is to thwart the jailbreak detection, which is not that hard when you have the game software to inspect to see how it's doing jailbreak detection. And you can also tell when the app is updated and then run the new version on a test machine to see how the new version is doing jailbreak detection.
It's hostile and a waste of time to do this when you're going to lose anyway. You only inconvenience the people who jailbreak their phones for completely unrelated reasons.