I mean, I saved up like 3000 gold just to play arenas and, not having all the time in the world, decided to let the bot have a go at some. Most of the time, the bot did not get pass 3 wins. Right now it is at 4 -2 only because I somehow have 3 legendaries in my deck - yes I had a ridiculous amount of luck in the drafts - and that leads me to think that I may end up at a whopping six. I am debating whether I am better off just trying to learn the arena, instead of being a lazy person (lol), and thus be more likely to get higher wins than is possible with the bot. Currently it sometimes times out on a turn due to the AI being too slow which, in the arena, is something that basically means you lose.
TL;DR: The AI is too slow in arena which means that you can get roped, and thus it never gets above 3 wins (usually)