So . . . I don’t actually think that USC, fine school that it is, is in the “same tier” as Yale.
Also, you think you want to go to law school now, but you could very easily change your mind. You may decide to go into consulting, or investment banking, or politics or any number of other things (and I’d urge you to keep an open mind about other possibilities – most lawyers don’t like being lawyers). If you want to change course and do any of the things I’ve listed, Yale will get you in the door more easily than USC.
Again, USC is a fine school and you can do anything from there. But it just is not Yale.