Okay, I'm a support main, but I love to play Kat so I'm going to give the most unbiased opinion I can give.
Kat, at least to me, is a very reflex-based champion. I rely nearly entirely on my reflexes to dodge stuff, be it just moving sideways (I have MS quints) or just Shunpoing out of the way of skillshots. That said, increasing Kat's cooldowns disastrously ruins her current style of play. Therefore, let's not even talk about changing that. This includes her reset mechanic. Lots of other champions have resets, it doesn't break the game.
Countering Kat. There are several ways you can counter Kat. Let me explain the most annoying ones I have to deal with when I play Kat. I'll start with laning since everyone should know by now how snowball-y assassins are.
Counter in Laning
When laning against Kat there are a few things the Kat player will be trying to do:
- Not get hit by skillshots
- Get as much farm as possible without using all her health pots
- Try to poke down the enemy mid laner to set up for a future kill
So at this point, its pretty obvious that most Kats will have a harder time against champions that have targetted or large area damaging spells, do high burst, are tanky, have good sustain, or are able to poke constantly.
Some of these champions include:
- Annie (high burst, targetted + area damage, decent poke)
- Ezreal (high burst, skillshot intensive, but great poke and can farm from range avoiding Kat's poke)
- Jayce (high burst, some skillshots but can gap close and does great poking)
- Diana (high burst, tanky, shields block poke)
- Swain (lots and lots of sustain, tanky, can easily kick Kat out of lane)
- Syndra (high burst; some skillshots need to land, but if the spheres are down, one area spell and Kat's stunned for a good amount of time; ult is targetted)
Playing any of these champions even semi-decently will make Kat think twice before doing anything at any point in the game. Winning the lane isn't enough however. Being a Kat player, whenever I am dealing with an opponent above that is successfully denying me farm and kills, I'm just going to roam. A lot.
Remember that an assassin can easily sustain themselves with kills instead of farm. Zoning them will delay them, but not stop their snowball. Therefore, know how to react when the enemy Kat is roaming. Alert the team when she's missing, make sure bot is warded at all times (bot is easy early double kill and will most likely be camped by a Kat, most top laners are horrible to gank as Kat)
Ganking Kat during lane
So many junglers make this mistake. It's super easy as a Kat to avoid a gank because of the mobility she has with her Shunpo (E) which teleports her to a target location. However, this ability has a LONG cooldown. Unless Kat gets an assist or kill, it'll be approximately 11-13 seconds before she can do anything useful. Kats only engage when E is up, and only can escape when E is up. Therefore, when ganking, let her use her E before you come to her! Most Kats at early level are using their Es to farm anyway, this is a perfect time to gank. Come from behind immediately after she wastes her E, and cc her to try to get a kill. Also remember, not having a target is not a reason to gank. Any semi-decent Kat can ward jump, and very fast. So always make sure to screw her over when she wastes it on a minion.
Highlighting the 3rd point on the first list above, Kat will try to poke the mid laner down. That being said, don't be an idiot and stick around in lane with 300hp or less... You'd be surprised how many people do this. They're confident because they're under tower. It's not safe. Kat snowballs really easily with an early kill. This means that most Kats are willing to tower dive at level 3 and use their flash to engage since if they're successful their escape is back up again. Don't stay in lane if you're low. No, I don't care if you want to farm more. A couple of minions is not worth dying to a Kat.
Counter during teamfights
Despite what many people think, stuns and hard CCs are not what counters Kats later in the game. It's the exact opposite.
You see, Kat, like any assassin, needs to choose the right time to engage. The time to engage is when at least one enemy is low and all CCs are used up. Keeping everyone at full health is difficult and everyone already tries to do that anyway, but using your CC is big. I'm not saying you should focus Kat. Not even that, just don't use a hard CC. The threat of a stun to a Kat is much more frightening than anything else. An Annie with a spiral flame on her will guarantee even the most fed Kat will not engage. Same goes for any 1-click ability that screws her over (Warwick ult, Blitz ult, Annie stun, Leona stuns, Janna tornadoes, etc.).
Obviously, if she does go in anyway, then blast her with CC. Kats are squishy, which means that if you keep her pinned down for 1.5 seconds or more, she's dead. Suppression ults are great at doing this. Vi, Warwick, Skarner, and Malzahar can all screw over a Kat.
Another thing you can do is end the fight early. Kat will only engage when she thinks she can kill. Which means that sometimes in long fights involving multiple tanks, Kat may actually be just on the other side of a wall waiting to engage. What does that mean? It means the fight you're actually fighting is a 4v5. End it early, try to not use up all your CC, and if you're low, back away from the fight. One teammate low is a threat to your entire team. This is against any assassin.
General opinion on other aspects:
Kat's damage is fine. In fact, Kat does very little damage at early levels. So low in fact that most people choose to play her with low mobility just to get damage early. Meaning AP quints instead of MS quints. They are easy to gank because of this! Not to mention they won't be able to roam a lot.
But the point is, if they're playing Kat right, they won't do damage at all early game. They will only get a kill if you are really really really low. (Don't get low). Kat's scaling however, does a lot of damage in her ult. This however is not OP. Why? Because no Kat should ever be able to fully channel her ult. Kat is super vulnerable during her ult and therefore shouldn't ever stay in one place for too long. A good Kat in a teamfight will ult for a splitsecond near someone who is nearly dead and immediately E+W onto the next low health enemy when the reset comes up. Specifically to make her hard to hit. If you deny her the first reset, she'll be sitting there for 2.5 seconds waiting to get out and won't be able to. And she'll die.
Kat's ult is fine damage-wise.
Cooldown on her ult? Was already nerfed. By quite a bit in fact. Kat would normally use her ult early game for extra damage even if it didn't kill, the cooldown was really low, and that was a good harrass tool. However, with the most recent changes, her ult cooldown at early levels actually can screw her over. If she doesn't have her ult up, she doesn't do damage to kill. Therefore if you get her to waste her ult in the early game, you're probably safe for the next 80 seconds or so.
Tips:
If Kat jumps on you, don't panic. Especially if you have a champion that has something you can use. Ahri for example can be used to screw a Kat over. Kat's most common harrass combo is Q + E + W and then run away with the extra movement speed. Repeating until you're low on health. If she does that to you as Ahri, don't panic. Remember that Kat's E will take her behind you (so don't shoot your charm straight at her when she's walking to you, it's a ridiculously easy dodge), therefore save your charm to shoot it at her after she lands. Not immediately after however. A good Kat will be expecting your charm if you save it, therefore let her run to the side first before trying to land your charm. If you land your charm on Kat during lane, you will do more damage to her than she did to you simply because Kat does no damage during the pre-6 levels.
If you're having a very difficult time with Kat, I suggest you play her. Playing a champion that makes you frustrated will help you understand her limitations. You will be able to better counter a Kat once you are able to play her decently.
Sorry for the long post, hope some of this information you find useful :3