Well sure if you put it that way, they're similar. But it's either you don't see it and you get surprised by increased quota usage, or you do see it and you know what it means. Bonus points if they let you turn it off.
Plenty of room for a middle ground, like a static timestamp per session that shows expiration time, without the distraction of a constantly changing UI element.
No need to gamify it. It's just UI.