One of the reasons why champions meant to build damage are building tanky now

Is because there are too many ways to artificially increase a champion's damage output while giving them tankyness. That is, there are too many items and masteries that increase a champion's damage output outside of this champion's abilities, while offering them a way to become tanky. For example, items.

Sunfire Cape gives a champion constant damage. Now that it has been buffed, allows a champion to waveclear easily, while offering defensive stats almost on par with Deadman's Plate.

Speaking of which, Deadman's Plate is a very good item for those "tanky" assassins and light fighters. Even though it has been nerfed, it still has that passive movement speed increase and the 100 physical damage on-attack. Those are too good to pass up, as they make a champion harder to kite.

Then there is also Iceborn Gauntlet. This item has been buffed to the point that it outclasses both Trinity Force and Frozen Heart, the items that it competes with for itemslots. Iceborn Gauntlet is generally better than Trinity Force because the latter, while offering more damage, is too expensive and doesn't offer any immediate tankyness. Also, it has 10% less cooldown reduction. For those reasons, Iceborn Gauntlet is generally a better item to rush. As for Frozen Heart, Iceborn is generally better because even though FH has more armor and a fantastic aura, the damage and slow from Iceborn Gauntlet are simply too good to pass up. This item does the job of both Trinity Force and Frozen Heart at same time while being cheaper than both and saving an item slot.

The only "damage" tank item that is shit now is Thornmail. It has been nerfed to the point that only full tanks that only build armor, or Malphite, Rammus, or Taric, can actually take advantage of this. However, most "tanky" assassins do not need this item to have a lot of damage.

Titanic Hydra, Sterak's Gage, and Maw of Malmortius are bruiser items, but they still give a lot of tankyness. Titanic Hydra allows any melee champion to have a damage source scaling with their tankyness, encouraging them to further build tanky. This is true even after the nerfs. Sterak's Gage was meant to be built on bruisers, but with the way it currently works, any champion can buy it if they want protection from burst damage. Maw of Malmortius is simply too good against AP champions.

Two items that deserve a special mention are Sated Devourer and Guinsoo's Rageblade. While they do not offer tankyness at all, they still artificially increase a champion's damage in some way, and on most cases, allow those champions to built tanky after completing those items. Sated Devourer doubles on-hit effects, allowing champions to rely on their on-hit effects to deal damage, and thus, build tanky items after, to survive better. Guinsoo's Rageblade increases the magic damage output of a champion, gives it too many stats, and even allows it to waveclear.

Another special mention goes to Spirit Visage. While it doesn't directly increase a champion's damage output, it offers cooldown reduction and increased healing. The cooldown reduction helps if you are a caster champion, for obvious reasons, while the increased healing allows champions with Grasp of the Undying to heal even more with this mastery. This is why most champions nowadays buy this instead of Banshee's Veil, as the latter does not offer increased sustain and CDR, on top of being slighty more expensive. While the latter has a powerful shield, nowadays, this shield is too easy to break, and its cooldown is just too long. The only two reasons to build Banshee's Veil over Spirit Visage are if you are an ADC, or if you need even more magic resistance on top of Spirit Visage and Mercury's Treads. This is almost never the case, and even if you need more magic resitance, at this point you either buy health instead or you buy Maw of Malmortius or Abyssal Scepter depending from how your abilities scale.

Outside of items, there are also other factors. Grasp of the Undying is a mastery that gives sustain to champions that do not have natural sustain, while giving them yet another artificial damage source that scales with tankyness. This mastery alone increases the laning potential of a champion significantly, and that's the reason why many champions previously with poor laning phase are now performing much better at top lane, for example, Ekko.

With all those artificial damage sources, it is not difficult to understand why champions previously meant to build damage are now building tanky. Combine those artificial damage sources, with high base damage, and you have a champion that can do the job of an assassin while being tanky as hell. And while most of them have little to no utility when compared to actual tanks, nowadays thanks to this meta, damage >>>> utility.