Having the really heavy weight toward the bottom would help a lot. You could have a couple of guys doing pull ups on a wall with that weight with no problem. The problem is they wouldn't be doing pull ups 24/7 for years. It's as much horizontal weight as anything. It's like you took a chair and cut the front legs off. There would be a lot of weight pulling horizontally. It may work and it might not. A lot depends on the strength left in the studs and if they are well fastened to the top and bottom plates. It would work in my parents house. The studs are a full 2"x4" and made of poplar. Another house especially if the studs had large knots or dry rot the studs might break in two. There is just no way to really answer your question. You would have to take the lath and plaster off the wall to really determine the structure of the wall.4 or 6 studs depending on which shelf is involved. No less than 4.
The only heavy shelf is the bottom -- 16" with the LPs.
Basically the same as two big guys doing pull ups on a bar attached to the wall. I've got 300 lbs on other walls and they seem fine.
But I take your point. I can put legs under the bottom shelf. Just seems inelegant.