For the parkour, they just need to start over from scratch.
Make it much more simple, much faster and, especially, add some level of agency to it, that isn't simply keeping a button pressed mindlessly.
Unfortunately, i concede that there aren't many good examples around (unlike combat and stealth, for which they have no excuse).
Infamous' is very janky and completely weightless, Shadow of Mordor is even slower than AC's and significantly more rigid.
The problem however is that AC's parkour is far too concerned (like many other elements of the game) with looking good, rather than being functional, deep or fun to play with.
You have about 1 million different animations, for a million different interactive ledges and poles, but at the end of the day you rarely feel in control, nimble, agile, when scaling around the cities.
More over, you rarely have to put any thought into it.
When i do some amazing acrobatic number in Super Mario 3d World, i feel like a fucking ninja, because it was me who avoided that missile, wall-jumped over the laser, and landed on the moving platform all in one, quick go.
In AC i'm pressing forward, RT and maybe A... there's a chance i'll see some fancy animation, or that i'll get stuck in some geometry, but my part in it, feels extremely limited whatever the outcome.
Of course i'm not saying they should apply Mario's platforming to the game (duh) but the principle of my reasoning, is that making controls that are responsive, agile and malleable, may not wield as fancy looking animations as AC has now, but would provide a much deeper gratification, when all is said and done.
They don't do as well for E3 vertical slices though, which is why i'm afraid Ubisoft will never changes things in this sense.