I don't think the idea is so much to limit Udyr by objectives as it is to bank even more on his current ability to clear jungle camps really quickly. Rushing an early Drake, for example, could give Udyr a true ability-based power spike, which he generally lacks past level 3, and the same could be achieved in the mid-game by going for the Rift Herald. For sure, a mechanic like that would have its drawbacks by not working so well on top lane Udyr, who'd have to roam to get a Drake, and it would feel shitty to lose out on so much power when the enemy's ahead and in control of either jungle camp, so it definitely risks generating some frustrating gameplay down the line.
However, I do think it could still be a means of adding an additional layer of strategy to Udyr, his team and the enemy by emphasizing objective control at different times, and so for not that big a cost in complexity (in fact, it could allow his current stat steroid to be funneled into his Q and E, which provide very similar stat bonuses, turned into base stat increases, or simply removed in favor of more visible power). By contrast, a gimmick is generally something that looks very flashy and takes up a lot of attention, but is very shallow in practice: only testing could really determine the actual depth to such a mechanic, but in terms of information overhead, it doesn't really have the same kind of minigame aspect as Fiora or Skarner's passives, nor does it bank as hard on a single feature as, say, Shyvana's dragon-based bonus resists.
With that said, I also like the simplicity and consistency of just giving Udyr bonus rank-up points at levels 6 and 11, and a major upgrade at level 16, as you suggested, which would simulate the power spike of an ult on a champion with only basic abilities. My main concern is that this kind of mechanic falls into power without gameplay, as Udyr wouldn't really have to do anything to get those bonuses besides level up like normal, but that could still be fine if Udyr were made to have more opportunities for gameplay and interaction elsewhere on his kit.