A guaranteed double shot would just be clunky and weird. Having the first shot do extra damage or temporarily increasing the tower's attack speed for the first couple of shots would be a better way of punishing aggression.
I certainly wouldn't mind it if the towers were more threatening in the early game. Give them a buff that lasts for the first few minutes that amps their damage to champions so long as a friendly player is standing underneath it, like:
- "Outer towers gain 50-10% (scaling down over the first 14 minutes) bonus attack speed when targeting enemy champions, decaying over 5 seconds and resetting after 3 seconds of not targeting an enemy champion. This effect only occurs if a friendly champion is within the tower's attack range."
This would make towers scarier in the first part of the game so long as they are defending someone trying to hug it, discouraging tower dives and making towers a safer place while still allowing people to get that last hit in under tower if they really want to (killing the champion means there's nobody to proc the higher attack speed). Tower dives are exciting plays, so they shouldn't go away entirely, they should just be riskier.
Make them do mixed damage as well. I'm tired of champions like Akali being able to build just a Zhonya's and suddenly be able to go under towers for free. Make 55% of the damage physical and 45% magical so that towers hurt everybody.