The Chase Mobile App Update solves the “issue” that I had with their badges.

Quite frankly, I disabled Push Notifications on the Chase Mobile
application because it was like jumping through hoops just to view the
actual notifications in order to clear the badge. It shouldn’t take
that long to access the micky ficky.

But now, Chase Mobile App clears the badge as soon as you login.

Score!

…maybe they DO listen to their customers
…when it benefits them to do so. ;)