Kukai's argument is not simply an assertion that buddhahood is quick, it rests on a specific claim about what a person already is. In his treatise on attaining buddhahood in this very body, Kukai grounds the claim in the doctrine of the three secrets, the correspondence between the practitioner's own body, speech and mind and the body, speech and mind of the cosmic buddha Mahavairocana, so that ritual practice, mudra, mantra and visualization together, is not building a connection that does not yet exist but activating a unity Kukai holds was already there from the start. Because the identity is already real, what closes the distance is realization rather than accumulation, which is the specific move that licenses calling the path swift rather than merely asserting it.
Tendai's parallel claim rests on a different textual warrant entirely. Rather than an esoteric correspondence doctrine, it points to a single narrative moment in the Lotus Sutra, the daughter of the dragon king attaining buddhahood immediately and in her present form, treated as scriptural proof that instantaneous attainment is possible within the Lotus tradition's own canon without needing Kukai's esoteric apparatus at all. The two schools reached the same conclusion, rapid buddhahood in this very body, from arguments sharing almost nothing, which is why their centuries of dispute over the claim never resolved into either side adopting the other's reasoning.