a ) This is true. Mouse is faster and more precise than an analog stick can ever be.
b ) Shift state toggles solves this. It's easy to bind 50+ or even 70+ keys on a controller. I think I have ~40-50 now, but I can add more. Simultaneous inputs is a limitation to this solution.
The same sentiment is applicable to my keyboard. On my set up I have 17 abilities on key binds, and can then bind another 17 to shift+, another 17 to ctrl+, another 17 to alt+, and - due to my keyboard being awesome - I can also use the Win key for another 17+. That's 68 abilities on 5 shift states. And that's only using keys left of 6, T, G, and B, so there's a huge amount of space for yet more. As a matter of accessibility, the keyboard beat the controller as the keyboard can have more abilities on less button states.
I'd also hazard that the controller set up needed adds travel time to abilities, so you're losing anything up to half a second on casts. That might be OK in PvE, but when you hit a server lag spike and are having to deal with slight delays anyway... that's going to add to your problems in PvP. And before you go "there is no latency on button press", there is; I've tested it extensively across multiple games. It's slight, of course, but it's still there.
The range of motion that a keyboard/mouse allows you outstrips anything you can hope to gain from a controller. The placement of AoE abilities may well be "easy" on a controller, but you gain a lot more precision on a mouse. Precision is a key factor here as well, because it impacts so many areas of game play. There's a reason console shooters come with native aim assist in-built and PC shooters don't; that's down to a lack of sensitivity and precision allowed by controllers.
So if we're looking at a controller and tallying points based on a functional comparison between it and a keyboard/mouse, the controller does not come out on top.
The vast majority of people aren't playing to be bleeding edge. They're not going to notice a slight delay on button press. They're not going to want to key up more than 30-40 abilities. They're not going to want endless precision on their AoEs. Most people playing the game are going to be playing casually. They'll want to sit back and relax into the game; the controller certainly serves this function well.
So if you want to use the controller, feel free to do so. There's absolutely nothing wrong with that. However... don't try to claim it is allows comparable levels of control and precision to a keyboard and mouse set up, because it really doesn't.