Kyuubi and Naruto are buds, Kyuubi hates being subjugated, and nowhere have I ever seen it implied that Hashirama could control perfect Jinchuuriki or suppress their chakra, Now Bijuu on the other hand he could control like his pets, and Yamato and company only tried to suppress an out of control Naruto, it's basically the Bijuu in control.
Hashirama's Bijuu controlling powers won't help him because Naruto and the fox are in unison instead of their love hate relation ship. Naruto has unreal chakra levels, and he's a jinchuuriki. Bringer of Darkness is useless because genjutsu is nothing to a perfect jinchuuriki. Honestly BM Naruto with a half dozen KM clonez and a sage mode clone is enough to beat any ninja on the show.
The Fox knows about Hashirama, and will be dropping Intel on him the whole fight, Naruto would have to be blind deaf and dumb to lose to Hashirama with all his power at the moment