if your user interface requires something to be visible constantly WITHOUT reloading or refreshing, a frameset is what you SHOULD be using
Had you written 'there may be a small number of scenarios' where framesets represent an optimal solution i.e. possibly better than using pop-ups' then I'd have been less inclined to disagree. In the case of video or audio which needs to play without interruption you have your scenario, granted.
Taking the example of Online banking I can only say that Barclays and HSBC don't use framesets so I don't buy that scenario especially as the bank controls both the navigation and content. A frameset also potentially allows connections to third party untrusted sites without a user knowing it as the browser still shows the keylock symbol.
Will browsers continue to support frames on desktop for some time - probably - on mobile browsers I wouldn't like to bank on it.
Getting back to the context of the OP and unique scenarios aside - don't use frames as they are bad for accessibility and present usability problems. Here's some more for the list:
1 - they screw up bookmarking to as you can only bookmark the frameset and not the pages within the frameset. If you do manage to bookmark the page within the frameset then when you go back to it you end up on a page that isn't meant to be displayed on its own.
2 - they screw up printing
3 - they screw up sharing - you can't share a link which shows anything other than the original frameset url
4 - they introduce an unnecessary level of complexity for developers
5 - unexpected browser back button behaviour