I never stated this, I stated that his increased reaction speed enabled him to react to Kaguya's portal with impeccable timing whereas Rikudou's chakra enabled him to accumulate greater chakra with ease, enabling him to activate Kamui earlier as well. Logistically, Kakashi w/o Rikudou's chakra wouldn't perform a high-end feat because even with DMS, he's still far below that caliber.Rikudo chakra doesn't speed up warping time lmao and that's obvious the only thing that speeds up the warping time is DMS alone and that was confirmed here[You must be registered for see links]. It will time him out? No it won't since he wouldn't need to be intangible for 5 mins straight when he can warp out of the pollen range or use his giant Kunai to cut down the branches.
Also Hashirama is sniped before he can even weave a hand sign.
You're correct, there's likely a greater time-limit, but attempting to blaze through the entire forest will leave him susceptible to Shinsuusenju and he's still open to reinforcing his Flower Tree World with even more Mokuton regardless.