Oh yes it does have a high cool down too. I was just stating DF because you said DF (and DF only) was difficult to punish so I commented on that. Both moves are easily punishable. Since DF is 41 Frames and Gungnir is 55 frames Gungnir's cooldown is higher but it doesn't really matter though since they are both punishable.
There is no correlation between startup frames and cooldown. There are a number of moves that have higher startup but lower cooldown compared to faster moves. Using Kain as an example, Cyclone is his longest startup BRV move, but has cooldown comparable to Spiral Blow, and Lance Barrage has longer cooldown than Celestial Shooter and Crashing Dive, which both have 2 more frames of startup. Other characters are pretty obvious about it too, like Cloud's Slashing Blow and Aerial Fang, Gilgamesh's Whirlwind Slash, Sephiroth's Oblivion, most ranged BRV moves...Dragon's Fang has less cooldown than Gungnir because it is programmed to have less cooldown, not because it has less startup.