OP, Naruto, Toriko are the three front-runner when Jump promotes their magazine.
though there isn't really a "big three" anymore, because that was a unique time when One Piece, Naruto, and Bleach were all the most popular Jump manga/anime in the world, much more than any others.
But these days, Bleach has ended as an anime, and lost popularity in Japan. and One Piece is just now so freaking far ahead of anything else, it doesn't do it justice to call it a part of any sort of triumvirate. Meanwhile, everything anime has lost popularity among casuals in America. whereas the actual anime/manga fans are much more likely to know about more things. JJBA was huge when it was airing, now it's SnK. meanwhile Naruto and Bleach have garnered a large hatebase, and probably OP to an extent.
so in my opinion, "Big Three" will always refer to those three manga. it wasn't that they were the top 3, or the best in japan, or the most known in america, it was that they were all of those things. Toriko is unknown in the west, and it's actually not very popular online. I think people need to stop getting hung up on deciding which series are in the Big Three, because if there's any debate you can be sure it doesn't belong. this sort of thing should be self-evident. it's like when Bush tried to declare Iran, North Korea, and Libya as the "Axis of Evil". which looks like an incredibly sloppy and arbitrary axis compared to the Germany-Italy-Japan one.
I actually agree with what you're saying here but I think the Toriko fanbase is still growing online but … not very connected because from what I can tell it's not as tiny and obscure as it used to be. ...Though you're right it's not super popular at all online or in "the west" as you put it.