Also, it depends on which Akane are we talking about. Are we talking about rookie-cop Akane from season 1 or are we talking about the skilled detective and leader of division 1 later, though one could argue both would be equally doomed. I mean, Makishima knew who Akane was before their first meeting, when she was still a rookie, which basically means her identity was publicly accessible. And for as brilliant as Shinya Kougami is, the same could be said of him. He was an inspector before he was an enforcer, and his name was out there for a while.
Both Akane and Shinya are great detectives. But the reality is, both of them are doomed against Light by virtue of the fact that they are public figures. The only thing keeping them alive is Light's own hubris; and as soon as it became apparent he was being challenged by them, they're both a pen stroke away from death.
If their names could be hidden from Light, it's likely they could both be a threat as time went on. Shinya Kougami has more experience than Akane when it comes to detective work, but you'd be vastly underestimating her if you think she couldn't figure the case out or rise to his level. Season 2 and after Akane internalized the lessons she learned from Kougami to the point that she became downright brilliant. And she has Joji Saiga on her side, the professor who trained Kougami in deductive reasoning and profiling, and even Joji told Akane that she was fast becoming one of his best students. With enough time on the job and with every new installment, it's becoming increasingly apparent that she has what it takes to rival Kougami. Even he's acknowledged it.
Ultimately, the difference between the two is that whereas Kougami is willing to kill, Akane is not. But then, this limitation isn't much of a weakness for Akane, because even though she's limiting what she'll do, it enables her to often come up with other far more creative methods to get her way than Kougami would consider. Kougami is brilliant but he tends to resort far too easily to that tempting option of killing his opponents, or at least personally going after them, even when it'd be smarter not to-- or even when his brain is telling him its a trap or diversion. He simply doesn't care and pursues his foe like a hunting dog.
And that's because even though he is "free" to kill, he has a limitation few pick up on in that this man suffers very personally from a hero complex. Justice has to be done his way, by his hand. It's not enough that the bad guy is stopped or that some other entity takes care of it. But hunting dogs and men suffering from pathelogical disorders are predictable. And Light could very well pick up on that and use that against him in the same way Makashima did. While Akane may not be willing to put Light in the ground if the guy is asymptomatic (and there's always that possibility when dealing with psychopaths in the Psycho Pass world), she is free to find other solutions; whereas to Kougami, Kira is just a nail and he's the hammer. It's hard to tell whether Kougami could restrain his impulses and listen to his brilliant brain long enough to find a way to get what he wants without falling into that familiar trap.
Now again, all of this-- ALL of this-- assumes Akane and Kougami's identities are completely hidden from Light's reach. It's important to stress that has to be possible or neither of them have much of a chance. But assuming that, both are smart enough to be able to solve the case and track Kira down by weighing the evidence.
And it's equally important to note that even if Kira was asymptomatic, he would INEVITABLY leave clues. L caught on to him because Light's pride prevented him from doing the smart thing and not getting baited into a game of one-upsmanship. He simply can't allow anyone to be smarter than him and ihas to prove it to everyone. And as a result, he is just as pathelogically addicted to a game of intellectual cat and mouse as Makeshima is. People like Akane and Kougami WOULD show up on his radar and he couldn't help himself but be drawn to prove he can beat them.
