Udyr and Phoenix Stance

Since hardly anyone ever talks about Udyr (who's my favorite champ), I just wanted to put out this thought that's been rattling in my head awhile.

Udyr is a unique champion who has no ultimate ability, and instead has four basic abilities that can each be leveled five times. However, the max champion level in only 18, which means Udyr can never max out all of his abilities. He can either do two 4 and two 5, or three 5 and one 3. It's generally better to do the later (because he only really needs three abilities for optimal play), and it's almost always Phoenix that's going to be left at 3. Phoenix isn't in any way bad, but it lacks the synergy that Tiger has with the rest of his kit. Udyr is a pure melee champion who's reliant entirely on on-hit abilities. As such, AD, AS, and MS are his preferred stats. Tiger strongly scales AD, and gives a free massive AS boost too, which in turn makes all his other abilities work better. Meanwhile, Phoenix only has low AP scaling, and really doesn't interact with the rest of his kit at all.

The question I keep wondering is what could be done for Phoenix to make it better for Udyr? Does Phoenix need to be reworked- or replaced entirely; or would it still be fine if he could simply max all his abilities? To that end, why not turn Phoenix into a starting ultimate like all the transforming heroes? Or if you wanted to keep his unique (possibly outdated) kit style, maybe give him two ability points at level 1 and 18 to round it out?