Before Udyr's rebalance, he had that exact function along with a mana return. It made turtle a first max requirement before it would fall off late game because building tanky gave it less of an impact. Maxing it early gave him an obscene amount of sustain in the jungle, but also pidgeonholed him into building heavy attack speed. This doesn't help his alternative role of being an amazing pusher. In fact it even hurts tiger stance in terms of its usefulness.
Honestly, as an Udyr player, I prefer being up to functionally use lifesteal/damage items in the late game and being able to max an alternative spell that isn't turtle first. Building ravenous hydra gives him a sizable health return with spirit visage, the rest of his build can even settle on being tanky and actually being useful in the late game.