What I want to say is 
. Her damage is toooooooo focused on ult that her power is completely decide by the amount of CC on enemy team. I'm not asking for real buff but can we shift some damage from her ult to her small abilities?
There are some pretty big consequences for doing that.
Firstly: take away it's damage, and Katarina's ultimate is objectively atrocious.
Self-CC, a self-centered AoE is not something you want on a squishy/semi-squishy assassin, a 3-target max cap is pretty depressing when you consider very few other champions have such limitations, and being a channeled skill opens up the possibility that it can go on CD while doing anywhere from 0, 20, 40, 60, 80, 100% of it's max damage potential based on how soon it's met with CC. Opponents can also walk outside of the radius to stop taking damage.
The only thing that makes Katarina's ultimate a useful skill is the impressive level of damage it can deliver to offset all those weaknesses.
Move Katarina's damage from her R to her QWE and you make Katarina's ultimate substantially less useful. Easily to the point it doesn't really feel worth using and her build and play style changes dramatically because of it.
Due to how objectively terrible Katarina's ult is what with all it's draw-backs: correct use of her R actually does take a decent level of skill and patience and it's optimal useage is the big skill divide between good Katarina players and bad Katarina players when it comes to Katarina's mechanics.
Secondly: Katarina's ultimate offers the vast majority of Katarina's counter-play and is generally the most interesting skill to play against and play around for Katarina's opponents and her teammates.
Bouncing Blade being point-click, capable of exceeding 1500 range with max bounces, being capable of turning anywhere near the minion wave into a danger-zone, and it's RNG element concerning bounce prioritization leaves that skill with pretty minimal counter-play options.
Shumpo instantly teleporting Katarina gives it phenomenal power in regards to evading skills, particularly the long wind-up/slow missile-speeds of most CC abilities.
And while Sinister Steel can indeed miss and is essentially a skillshot because of it, pairing Steel with the same kit as Shumpo makes it more or less point-click unavoidable damage in practice.
Ultimatly: Katarina's QWE lack a lot of meaningful counterplay options and chances for interaction, which would cause a greater portion of her kit's power placed in her QWER to make her feel even more like a low-skill, button-smashing, facerolling, pub-stomping champion.
Katarina did actually have her power shifted to her QWE at one point: right after her rework that replaced Killer Instincts with Sinister Steel.
She shot up in play rate, and playing against her was fairly similar to how playing against Fizz has always been: miss ult but doesn't matter, can kill with just QWE anyways.
After a series of patches, Riot moved Katarina's power back to where it is now: almost exclusively in her ultimate.
Or give her somewhat outplay potential like Yi's Q, I don't mind if her refresh or damage is nerfed
That's not really outplay potential so much as a:
"I suck at actually outplaying someone by using basic game mechanics and need a training-wheel skill to even think about outplaying my opponents"
kind of deal.
Wukong's Decoy and Fizz's playful trickster are in the same boat.
Being able to completely shut down an opponent's kit by retroactively avoiding everything with potato-like reflexes isn't out-playing an opponent so much as it's having an omnipresent counter similar to super-effective damage vs. an opponent. Such abilities allow one to win due to reasons that specifically have very little to do with play-making or skill.
Especially in the case of champions like Fizz, Yi, and Wukong vs. any range of squishy champions: if you wait for them to use their evasion they have enough time to reach you and OHKO you, if you don't you're full QWER can wind up doing 0 damage to them. As-such, main way to deal with them is more like dealing with a raid-boss in Wildstar where everyone takes turns blasting CC at them until something sticks. Or you just hope they're bad and waste their low-CD evasion for no reason when you're actually close enough to take advantage of that lapse in judgement.
But that (lack of) interaction is pretty much why pub-stompers stomp pubs and are kind of ~meh in the competitive scene.
Vs. a team that's always mobbing around together than black-and-white difference between CC them constantly to shut down their BS or don't allow skill to have much of a say in their BS auto-winning vs. the opposition without good teamwork and coordination.
With Kat her kit at least isn't training-wheels and she has a lot of risk involved to offset her potential reward. Mostly from being extremely ult-reliant.
TLDR: Pretty sure both of your suggestions would make the pub-stomping/lack of outplay potential worse in regards to Katarina rather than better.
