Why isn't Master of None season 3 does indeed feature a cameo by Ansari, but there are two main reasons why the storyline doesn't center on his franchise character.
Subtitled "Moments in Love," Master of None season 3 follows the love life of Denise (Lena Waithe), a character who appears in the first two seasons. After releasing her debut novel, Denise experiences all the usual challenges that come with success and trying to maintain a healthy romantic relationship. Master of None season 3 co-stars Ackie as Denise's partner, Alicia. The Netflix show's third installment was directed entirely by Ansari, who co-wrote the five episodes with Waithe. Previously, the duo won a Primetime Emmy Award for their collaboration on the Master of None season 2 episode "Thanksgiving."
Ansari isn't the main star of Master of None season 3 because he's ready to move on from the character. After season 2 released in May 2017, Ansari revealed (via Vulture) that he didn't "have anything else to say" about Dev Shah, and noted that he would have to "become a different guy" before reprising the role. In January 2018, Ansari was accused of sexual misconduct and subsequently put his professional career on hold. He also didn't take on another TV acting role prior to the release of Master of None season 3. Given that Waithe and Ackie are the main protagonists in season 3, it seems that Ansari is indeed ready to move on from Dev Shah.
In July 2019, Netflix released the stand-up special Aziz Ansari: Right Now. The 2019 Netflix special, Ansari acknowledged that he'd been trying to evolve as an individual after processing the sexual misconduct allegations:
"There’s times I felt scared, there’s times I felt humiliated, there’s times I felt embarrassed. And ultimately, I just felt terrible that this person felt this way. And, after a year or so, I just hope that it was a step forward. It moved things forward for me, and it made me think about a lot. I hope I’ve become a better person. I know this isn't the most hilarious way to begin a comedy show. But it’s important to me that you know how I feel about that whole thing before we share this night together.”
Prior to Master of None season 3, Ansari previously directed six episodes of the Netflix show. While it remains unclear if he will return to television or movies, it does seem like he's ready to move forward with his filmmaking career. According to Waithe (via Variety), Ansari is trying to move forward with his career without drawing attention to himself on camera: “He’s always really wanted to be in the director’s chair... And I think this season is a really big swing for him. It was not the easiest thing for him.”