Could Turrets attack Champions faster?

One of the problems with turrets in League, is they just seem to do so little. They are easy to kill and don't do much damage. However, increasing the defensive stats of turrets would most likely lead to games stagnating, as the higher defenses of a turret keep it from being destroyed, and teams could just stall games. At the same time, you can't increase the damage per auto of turrets, since then people can't farm under turret, a necessary part of trying to come back after losing lane. With these in mind, I propose that turrets should have increased attack speed, only when targeting champions. The AS stat would scale with game length, something like this:

0 - 5 Min: 10% increased AS 5 - 10 Min: 20% increased AS 10 - 15 Min: 30% increased AS 15 - 20 Min: 40% increased AS 20 - 25 Min: 50% increased AS 25 - 30 Min: 60% increased AS

Capping out at 70% increased AS for 35 + minute games.