mechanical compulsion

The morning after Letouse's murder, Klavier greets Apollo and Trucy at the WAA, asking them to defend Machi. When asked why Machi was arrested, he tells them:

"It was tough for me, too. We performed together that night, after all. Yet... The powers that be say that, given the circumstances, it could only have been him."

At NO POINT does Klavier ever say that HE believes Machi is guilty. Across the course of the trial, we get the feeling that Klavier clearly doesn't agree with the arrest, as he keeps bringing up these "powers that be" and how they want the case resolved quickly.

"Lamiroir was invited from Borginia as an ambassador of goodwill. It is vital that this case be wrapped up swiftly. That's all the powers that be want, really."

Klavier, and for that matter, Ema, KNOW that Machi can't have killed Letouse. Ema was the one who told us about the power of the revolver in the first place! And we later learn that Klavier never truly believed Machi was guilty, and suspected Daryan from day one (even if he was reluctant to believe it), having already submitted the paperwork to call him as a witness just incase.

The police had to rush the arrest, and Machi was the only possible suspect. With our initial knowledge of the murder, it took place during the 3rd set, when Klavier and Daryan were onstage. Apollo and Ema were guarding the door and saw nobody exit the room. Machi is the only one who could have entered and exited through the vent. Even if it's unlikely, and Machi wouldn't have been able to shoot the revolver unscathed, it was the only possible explanation at the time. (And we know by now that the judicial system in Ace Attorney is flawed - they'd rather pin the blame on someone, ANYONE, to resolve the case quickly rather than extend the investigation. It's not poor writing, it's the unjust nature of the judicial system.)

Both Klavier and Ema are under pressure from higher-ups and the Borginian Government to wrap the case up quickly. We can clearly see across the case how stressed they are, both being snappier and moodier than usual, but we don't know exactly what's going on behind the scenes besides what Klavier hints to us.

Their hands are tied, and they're forced to accuse Machi even if they don't believe it, because it's the only way that they can discover the truth, with Apollo's help.

They need Apollo to help them work out the order of events in court and find a breakthrough, so they have evidence to implicate someone else and can push the trial for a second day.

(Also, I think it's important to remember that KLAVIER was the one who asked Apollo to defend Machi. He implies that the request came from Machi, but considering Machi can barely speak English (and even Lamiroir wasn't aware he COULD until the final day of the trial) and Klavier's Borginian is extremely limited, it's easy to infer that Klavier made the request himself, or at least suggested Apollo because he wanted an attorney he could trust to help him uncover the truth.)

'Apollo Justice' takes place during the 'Dark Age of the Law', and is a game shrouded in darkness. From forgeries, to high-profile culprits like defence attorneys and interpol detectives that seem impossible to convict by normal means.

Serenade perfectly fits this theme, being a case where outside influences and political powers are so desperate to avoid scandals that they're willing to sentence a child to death. How the legal system is so flawed and desperate to find somebody to blame that they'll happily convict a scared, supposedly blind child who physically COULDN'T have committed the murder.