We haven't seen other level 5s than Accelerator, Biribiri, and Mental Out, if memory serves. We know Mikoto is no match against Accelerator, and we can deduce Misaki is neither as it's all too easy to imagine reading and affecting brain waves requires traffic to and from (Mikoto is able to block it, after all), plus she's even using that remote controller for whatever purpose. Besides, I don't see such a princess character interested in fighting swearing, scruffy men in dark alleys anyway. Mikoto was chasing Touma all the time to have a fight, but we all know her real tsundere motivation behind that action. She would never chase Accelerator similarly.

So, what guarantee do we have any of the level 5 would have a personality making them fight till death against another level 5 just for the sake of a ranking list? Nothing. That's just an assumption. Even Accelerator's personality wasn't deep down like that. If it was, he wouldn't have saved Last Order and suffer her continuous presence by living with her. In fact nothing suggests the highest level espers (4/5) became such by endlessly challenging strong people in fights. It's about personal reality, which makes it all about stuff inside one's head, not gaining experience points from last bosses.

I was never overly impressed by the people behind the level 6 shift program, so I've very high doubts the stupid fights Accelerator went through would serve any other purpose but to make him a psychopath. Seriously, the CPU time they got from Tree Diagram was completely wasted.