Well, with the common knowledge that every point of armor increases your effective hp vs physical damage by 1%, 4,000 hp + 3.5(4000) is gonna be about 18,000 raw health vs adcs. Now i don't know what adc's youre thinking of, but most of them cannot deal 6,000 dps to kill that kind of a tank in 3 seconds.
Your hyperbole is incredible, and your argument cant be taken seriously when you make goofy claims like that.
But if i were to humor this 6,000 dps adc, i guess he would have to have max attack speed. Thats 2.5 attacks per second, but he might need 100% crit chance too, just to come close. I suppose last whisper armor pen matters too. So vs last whisper, this tank now has 15,700 effective hp.
Thats 5233.3 dps, 2093.3 per attack, 837.3 before ie crits.
837.3 ad is infinitely unattainable for an adc who is also itemizing for lw, 100% crit, and max attack speed, and attacks of that damage are equally unattainable for Caitlyn or Draven or Kog'Maw or whoever.
And lets be honest, if you can tank an adc that is stronger than the game can even let them be for 3 whole seconds, you're doing your job as a tank.