The Lotus Sutra does not argue for the one vehicle abstractly, it tells a story. A father whose house is burning cannot get his absorbed children to leave by describing the danger, so he promises each child the particular cart it wants, a goat cart, a deer cart, an ox cart, to draw them out. Once they are safe he gives every child the same magnificent cart regardless of what was promised, because a father's wealth does not run short and the different promises were never separate gifts, only the means suited to get each child moving. The sutra glosses the parable directly: the three vehicles of the arhat, the solitary buddha and the bodhisattva are the three carts, provisional means taught according to what different listeners could grasp, and the one buddha vehicle is what every child receives in the end.
The parable does real argumentative work rather than merely illustrating a doctrine already stated. It answers the objection that a scripture teaching three different goals cannot be internally consistent, by recasting apparent contradiction as pedagogical sequencing, and it licenses every later school built on the Lotus, Tiantai, Tendai, Nichiren among them, to read the rest of the Buddhist canon as staged instruction leading toward the text that finally discloses the single destination.