Katarina's Current Balance, From a Kat Main.
My opinion on the current Katarina balance trend is, I don't think she will ever be balanced with her current kit and the current runes in combination. The only way to stop her from being totally OP with her current abilities is to nerf her into the dirt. There's going to be no middle ground between useless and OP. The new runes are plain and simply meant for Katarina.
The most pressing issue, she heals wayyyyy too much with the gunblade/ravenous hunter combo. On top of triumph heal.
Eyeball collection and triumph gold on takedown helps her snowball even more than she already does.
Electrocute, sudden impact, and coup de grace help her burst immensely, when she probably has enough without any of it.
Essentially, it feels as though the Domination/Precision combo were literally made for Katarina.
As far as suggestions go, I'd remove damage entirely on Shunpo. Slightly reduce base damage on later level q's. Increase damage on dagger pickups, while also increasing the time it takes for them to drop by about .25-.5 seconds. M A Y B E a brief .25 second slow on e to compensate?