ADCs don't just "dps you" with full items. They crit you for 800+ damage, over 1k with certain champs (draven, caitlyn passive). That's a lot more than most mages can you hit for. Mages also have cooldowns and most of them have to land their abilities, while an ADC just right clicks on you. In return ADCs have to deal with armor.
So what exactly do you think Cass should be able to do? if she has worse damage than an ADC, why not just go another ADC mid? Ryze, you have a point, and the new one needs to be "fixed" so he can't root you over and over and over again while destroying your entire team. Azir, eh. I havn't played against him enough to form a solid judgement, but I don't really see him "bursting anyone from 100%-0" unless he's disgustingly fed. Have you seen what a disgustingly fed Draven can do? What about a fed Kalista?
You say mages "have access to itemization that grants them durability, utility, cdr, and invulnerability." Durability and invulnerability are the same thing, but I'll grant you one of those. utility? Where? Supports and tanks have most of the utility items, Ii'm not really sure what you're talking about. Maybe rylais? But ADCS have access to phage / botrk / many more movement speed items. Also, saying their items are better because they give CDR is silly because adcs don't care about CDR for the most part. That's like mages whining that adcs have access to itemization that gives them attackspeed. Furthermore, adcs can easily get CDR if they want it via black cleaver (which is a great item), ghostblade, and / or blue boots / runes. Except they get berserkers, because they don't really care about cdr.
So, now we've narrowed it down to just durability (i hope). Why do they need more durability? Because if they can't one shot you, then they will die immediately to the ADC without durability. That doesn't sound like a very fun game... it sounds like a very boring fps. Better hope the rocket launcher hits them, or you will die to machine gun during reloading. Where are the pistols, the SMGs, the shotguns?