Making something the defining characteristic of a class is a thing riot is more than capable of. Champions still need to lane though - but that can be taken care of by utilizing conditional items.
So if i understand correctly, you propose if tanks want damage they should invest in damage items? Which if you do, shame on you. In order for a champ to lane, he needs damage. And if tanks buy damage items just so they will able to lane, is simply absurd.
Tell me what is assassin itemization? Marksmen? Mage? Fighter? Juggernaut?
Assassins itemization? For ad ones, every lethality item, black cleaver and currently, last whisper too. For ap ones, lichbane is the only core. Unfortunately ap users get the short stick in items with having the least variety.
Marksmen? Pretty much every crit item.
Mages, pretty much every ap item.
Fighters well have their items split in half. Divers buy a bit of hp, but they might invest to some items that give attack damage. On the other hand, juggies prefer tanky ones since they lack target access without flash. As such tanky items will help them survive.
Making tanks have a niche - PROTECTING ALLIES WITH MEANS OTHER THAN SHIELDS - would be the perfect way to differentiate tanks from bruisers and fighters.
Emmm what? Their role is to soak damage and provide crowd control. Braum, tahm and taric have the niche of protecting allies. Not every tank's job is to protect allies. And again, FIGHTERS (bruisers and fighters are synonyms in lol terminology) deal DAMAGE while also being durable (they also come with some sort of sustain) enough to walk to the enemies. Tanks have tons of relatively easy to apply hard cc while being durable.
Perhaps all "tank" items get the warmogs heart treatment
Riot doesnt want (or at least in the past, i dont know their current thoughts on that) to limit the items accessibility, unless they are breaking the game.