Tower Buff

So Towers are in a much better place now that true damage absorption was added, but the early game easy dives are still a pretty hefty issue, so I had an idea that might help those that are falling seriously behind and getting pushed to their tower constantly.

What if towers tracked minions they killed, increasing either their damage or attack speed for a duration based on the number of minions killed?

For instance, you die and the enemy lamer pushed the wave to your tower, they do this several times in succession before you can get back to lane, the tower has killed approximately 19-20 minions, therefore, it attacks either 20% faster, or does 20% more damage for a period of 30 seconds, at which point the minion buff stacks fall off one by one every second thereafter, until the tower kills another minion.

In the interest of keeping splitpushing at least somewhat viable, maybe the buff can only be active when an allied champion is nearby.