There's a difference between countered and hard countered. Most melee have gap closers or more potent speed boosts. Udyr's speed boost isn't enough for him to ignore slows.
Udyr is hard countered. Most other melee are not. They either have a gap closer, a ranged slow, or a more powerful movement speed boost. Bear Stance lasts longer than most speed boosts, but it doesn't give enough speed for him to catch his target, so it doesn't matter.
Consider a team fight where Udyr runs in and goes for Ashe. He's not going to be able to catch her, she's just going to kite him. Udyr is now in the middle of your tanks. If Ashe's team mates went past Udyr to kill his team mates, Udyr can't reach them to peel. Udyr also can't reach Ashe. The only target Udyr can actually hit is the enemy team's tanks, which is completely useless.
Morgana is a terrible pick and will never be seen in any remotely high ranked game. Synergy with obscure champions isn't an excuse to allow Udyr to be kited so easily. He needs something to counter kiting, in exchange for a damage reduction, because his damage is currently way too high.