The only thing I can think of, would be maybe by him "coming out", he would also be PROVING that God himself exists, too. Really you cant have one without the other, lol.
I am not saying this as fact, I am just following your train of thought, which I actually think is a good one. It does make sense that if Satan wanted ALL the power and glory, wouldn't he want to be front and center, idk.
There is the famous saying, that the greatest trick the Devil ever did was to convince the world he doesn't exist. Perhaps by remaining in the "shadows", he can control the world, and deceive humans away from God. Kinda like the "power that be", that conspiracy theorists believe TRULY run the world. They want to use a puppet government, while they stay behind in the shadows, ushering in the "new world order", while controlling the money and power.
OR, its all a bunch of bullshit, and is an ancient fable to help other men, control other men. If a priestly class can make other humans believe a Satan exists, and ONLY they have the power to save you from him, then they have control over those people. Sounds like what the evil slave, the Governing body, is doing to over 8 million people right now.