To simplify, we could say that until mid-Heian, spears (hoko) were the most popular polearms, mid-Heian to early Muromachi naginata, and mid-Muromachi onwards, spears (yari). Possibly accompanied by changes in battle from close-order, to open-order, and back to close-order. It's a bit complicated, because
(a) "hoko" is also used to mean "polearm" in general, as well as a hoko spear,
(b) "naginata" is literally "long sword", 長刀, and might refer to long swords in literature. References to drawing naginata (rather than "removing") might mean sword, not polearm.
At the time when naginata appear to have been the most popular polearm, polearms weren't that popular (the Mongol Invasion Scrolls have a couple of naginata, but the dominant weapons are bow and tachi (as a sidearm). So perhaps it isn't a case of naginata replacing spears for a while, but rather that spears just stopped appearing on the battlefield, and the few naginata had no competition.
Also, Kamakura naginata appear to have been much straighter than late naginata, and should not be hard to thrust with effectively. Looks like the more curved naginata appear when the yari does - instead of a single cut/thrust polearm, we have more a division into specialised cutting and thrusting polearms.
Don't know what any of that means for kikuchi yari. I haven't seen a kukichi yari blade of more than tanto length, so they're not much like early naginata.
Here's an Edo period socketed kikuchi yari:
http://www.e-sword.jp/sale/2013/1310_4035syousai.htm ; compare with fukuro naginata and you see a clear difference: this yari has a round socket, and fukuro naginata have oval sockets.
(Karl Friday says the difference between hoko and yari (other than sockets vs tangs) is that hoko have grippy hafts (spiral wrapped, not smooth) while yari have smooth hafts. You pool-cue thrust with a yari, not with a hoko. See "Samurai, Warfare and the State", and
http://www.e-budo.com/forum/showthre...ting-technique for his comments.)