This is ticking me off quite a bit (TOWER RANT WARNING)

Can turrets do any damage for the first 10 minutes of the game, please? I am getting sick of champions with just bami's cinder and boots tower diving while at 3/4 health, taking 5 or 6 tower shots and still walking out. This just happened to me in my most recent game and has happened a couple times before, also with bami's.

My opponent this game was poppy, she didn't even get her shield passive when she dove me. I was in lane as vlad, I got stunned by poppy after getting a cannon minion and lost 3/4 of my health from one combo (shouldn't have gone for it). She shoves the wave into my turret, tries to stun me against my tower, but I use my pool, she takes five turret shots (I counted) then kills me once I am out of my pool. She dove me with 3/4 health and walked out with 1/3 health left, (she was healed by grasp). She hadn't even hit 6 yet.

I understand late game you are supposed to protect the turrets but why the heck aren't the turrets able to kill someone within the first 10 minutes of the game? Watching the turrets, they don't even appear to be ramping up in damage. You'd think after 3+ turret shots they'd be dealing a significant chunk of health. No wonder people keep calling towers wet paper towels.