you can only push if there's no champion from stopping you
Killing champions isn't the only way to have none stop you.
There's a few awesome features called:
-Assists
-Harassing
-Striking fear into the 1-2 champions as 5 people rush the tower
-Taking major advantage when they go back to buy items
I've won games (and not bots either) where we only had 20 kills to their 80. We killed more towers (which give more gold than kills by the way, team game), got baron 3 times (which gives more gold than towers), farmed better, and despite the large number of early game kills they had, we were wrecking them.