I personally don't think Controllers are a handicap anymore as far as they have come, but using them exclusively for shooters will not allow you to ever become better at FPSs because you are indeed limiting yourself to what the controller offers and what it does hold your hand with.Better in what way though? Is switching to an input method that's perhaps more difficult really needed to become better? Does mastering the mouse make you a better player than master the controller?
I feel like this question isn't really sensible because, in a way, when you switch input methods you are playing a different game. Evidently, being good with a controller doesn't make you good with a mouse, and vice versa. They are two entirely different sets of skills. Unless there's absolutely a ton of aim assist on the controller, which one is harder to master seems very subjective.
The only thing I have to say on it is that if someone was completely new to FPS gaming and got to choose, I'd recommend them to go with mouse and keyboard. Why? Because I believe the aiming system there is more intuitive to learn. But if a game has both input methods set up and balanced well? I don't think it really makes sense for anyone to switch from their preferred input unless they want to learn something new.
SO While I DO agree that K&M is superior to Controller, it takes far more effort and work to get better at it than it does with a controller, so people saying they need the handicap for controller need to use K&M and realize how hard it actually is to use...I think a lot of this comes down to your background. You moved from consoles to PCs, so you had a reference point for how good you should've been, unlike when you were learning to play on a controller. Someone with a PC background could arrive to the opposite conclusion. I've personally had experience with both for a great part of my life, though I've played more on a controller because of Halo. Honestly, I don't think either method felt inherently more difficult to get better with. Perhaps the mouse felt a bit easier as a total beginner because it's just more intuitive, but once you become adequate, I really don't see a difference from personal experience.
One thing I think deserves to be mentioned regarding aim assist and bullet magnetism is that whenever you ask a competitive Halo player, they always want one thing: less. You'd get few Halo players to agree that there should be none at all, but many would agree that what there is now is unnecessary.
Here's a funny story actually, my very first experience on a PC FPS was DOOM, and I played it exclusively on keyboard, never touching the mouse (as crazy as that sounds). But as a Kid I made it work and beat all games in the series that way... Wasn't until years later when I got Halo for PC that I actually started using a Mouse to play FPSs on PC, but I digress...
To answer your question, once I switched from controller to K&M, my reaction time became significantly better as did my twitch reflexes and precision as to where to put or keep my crosshair. Keeping in mind the spray patterns of weapons also became something important because I no longer had magnetism helping me out... Most importantly, my ability to lead projectiles and hit them consistently improved tenfold.
This however took the course of 5+ years, between adjusting and re adjusting my sensitivity (and now Mouse DPi), as well as my movement habits... Something I cannot say I ever would've had to worry too much about in a console FPS had I still stuck to using controllers. Being able to jump and aim at the same time was also HUGE for me, especially since I could not afford any fancy controllers at the time and I could not get used to Bumper Jumper over Default/Recon...
By the way, I am not saying that controllers are in any way, shape or form bad... if an Elite controller player can get good enough with a controller to compete with a K&M player on equal footing that is totally fine... but I'm just saying that K&M pretty much forces you as a player to improve in order to get better in shooters because it in no way holds your hands, which IMO automatically makes it better than a controller.
Like I stated before, if you put the world's best Controller FPS player with the World's best K&M FPS player, but you still allowed the controller player some level of aim assist, can you really say the controller player is more skilled? even if in a match they're almost if not completely even? Surely you must understand why this topic has been so divisive for many years... People just don't like the idea of someone having any semblance of assistance being on equal footing to someone who has had to work hard to get to the skill they've gotten to.
You could argue that this is an elitist and honestly worthless mindset to have, but at the same time I can somewhat understand where these people are coming from, as it is the same reason cheating/aimbotting is so heavily frowned upon... Perhaps someday we won't have to make these kinds of arguments anymore, but the only way that's gonna happen is if crossplay between consoles and PC continue to be pushed, as we will never truly know how far we've come until the boundaries are pushed...