Could Katarina go top lane?

She could, but it is not really optimal, IMO. She'll have difficulties with killing the enemy top laner, and being stuck on one side of the map denies her the roaming capabilities in the early to mid game.

most champions would crush her in a 1v1 in top lane.

you'd get dove by tryndamere on the cooldown of his ult riven would 1-shot you lissandra would wreck your face irelia would destroy you

can't really think of any toplane matchups that kat would win.

I've played her top, you basically spam W on the enemy laner for a while but start to lose when they get tanky. Also if they have any CC its pretty much over.

Play Tanky Katarina jungle, buy the thing with the slow.

Build sorta tanky-AP

She can, but top laners tend to be tankier than your average mid so she is really better off in the mid lane where she can get fed.