Less information, true. However, you can't downvote submissions, so the graph will be rather boring. Just a ton of upwardly sloping lines, some sloping upwards faster than others
You could show the rate of voting instead of number of votes.
I'd guess that wouldn't be much different from the rank.
I think rank is actually more interesting. It shows how much "visible" is an item, i.e. its potential/relative popularity along with its current one.
You could draw a window around the visible items. It would show off relative popularity and rate of change as well.