One could ask the same question about Perry Mason or Arthur Kirkland. Mostly it's because either he knows the suspect personally and vouches for them even when the suspect insists that they don't want a defense (there are always convulted reasons for this, including the suspect legitimately thinking they are guilty), or the evidence accumulated feels... fishy. As in, you know that, "I notice that I am confused" feeling? That's it, in-universe, AFAIK.

Out-universe, some of the least passionate cases become interesting simply because of how curious we are about what actually happened. We notice there is untruth, and we want to dissolve it. We don't really know our client is innocent, but we're not sure they're guilty, and we can't let them get sentenced just like that, so we investigate, and the truth will be whatever it'll be.

That, and the character designs and mannerisms are really unsubtle for the Genre Savvy, you can usually spot the killer from a mile away if you know your tropes right. Though the games still manage to surprise you every now and then.

why doesn't the prosecution use whatever mechanism he uses to filter out innocent suspects

If they could, they would, so we should expect it's something that he has easy access to and they do not have easy access to. I am tempted to say Phoenix Wright's ability to be confused by fiction - it would be very difficult for the prosecution to use Wright's brain to filter out innocents.