Title. Champions like 
It seems like it gives good stats that all of them love, they've got plenty of spammable abilities to proc the sheen, and phage passive is great on any autoattacking champion. So why is Triforce bad on them?
Matezoide5 votesTrinity Force is core on Lucian, isnt it? Kog also builds it sometimes.
Anyway, the reason for that is because Trinity Force is extremely expensive and, even though it is a great item on pretty much every champion, just outclassed by other, similar options.
Of course Trinity Force on Vayne is a threat, but most of the time, she just cant really afford that item, and even when she could, something else might be more useful.
GundayMonday1 votesThis is spot on. Adding to it a little.
Think about what an ADC player's job is (Like why the exist in the meta). Basically their primary job is to output the most damage per second possible on towers (I know there are other jobs, but this is really why ADC as a role exists in the meta). In teamfights, you're supposed to be the last one alive so you can wreck the enemy base once everyone else is dead. You could buy a triforce, but there are other items that let you take out towers faster, that are easier to get, and also allow you to survive your weak early-mid game until you hit that late game ADC powerspike. So yeah, it's good, just other things are better and easier to get.
xo Violet1 votesIts a core on Ezreal and Kog'Maw. Lucian pretty much never builds it anymore. It's not built on Vayne because other items are stronger and synergize better with her 'W' which of course is her primary source of damage.
YumaS2Astral1 votesI don't consider it to be core for Kog'Maw, I build Statikk Shiv instead, it is cheaper and gives waveclear
TeemoJenkins1 votesI wouldn't say it's considered BAD on them, it's just a super pricey three expensive item kit, where other utility can be gained from getting other items.
SaltyKracka1 votesLucian is currently weak, and his passive (which is where most of his damage is located) scales better with crit.
Draven wants to not be casting spells besides his W, his mana pool's weak.
MF's damage is all tied up in her W passive and ult, and I think only her Q does on-hits.
Sivir has better things to do with her items, and she doesn't have spammable spells.
Vayne wants different things (i.e. attackspeed and lifesteal, and nothing but)
Pros build triforce on botlane Kog, though.
AMYS GRAVE1 votesMF and Sivir have high mana costs so they can't spam their abilities to proc the sheen.
Drunk Rummate1 votesKog does build trinity as a standard first item in his ADC build.
Vayne likes BotRK instead because the AP is a wasted stat and it gives more attack speed which she prefers, plus the sustain and active is nice.
On the rest of those champions TF is okay, but IE is just so damn efficient right now that you're pretty much forced into buying it if you want to be relevant midgame and once you have IE it's more efficient to build an item with higher crit like PD/Shiv over TF.
YumaS2Astral1 votesActually the reason why Vayne buys BotRK first instead is because the passive has synergy with her W
coeurloyal1 votesI'm not sure that Trinity can really be a 'bad' pick per se, but it certainly isn't the most optimal choice in every situation. Providing a boost in pretty much every stat means champions that don't capitalize on every stat (which is most of the pool) can't use it as efficiently as other items. It's strong, but typically not gold efficient.