The mage is not instakilling you with sunfire lmao. The HP from the item alone will fuck them while you build MR. As long as you don't build two armor items back to back, you're fine.
And the reason they don't have a go-to item is because a lot of tanks are different and they have options. You don't need to deal with the mage right away, unless you're actually laning against them, so you don't need MR right off the bat. You also don't have to deal with the ADC right away, and they probably aren't going to be killing you that early on unless it's one of the very few early-game ADCs, and they certainly won't be instakilling you.
And even with what you listed, it's not universal. A lot of mages don't use Luden's, IE is useless on Kog'maw and some other ADCs, and isn't always the optimal choice even on those who can build it, and AP assassins and bruisers both exist. Like...you didn't forget Akali, Kat, Diana, and Mordekaiser were all champions, did you? 3 of them got pretty recent reworks. I'd forgive you forgetting about Kat, since it's been ages since I've seen one, but there's no way you forgot about Diana having just been reworked.
And then there's non-AP bruisers like Mundo, who can't use BC or Trinity...
And then there's whatever the fuck Singed is...
Also, need I remind you that Titanic is an item? Basically nothing but HP and damage, scales with your HP, gives waveclear...
You have 4 fucking options, depending on the situation. All of those champions have 1-2 options.
Source: I play literally every role. Including tanks. Including toplane tanks.