Satan is permitted to exist for the same reason anything is - God’s sovereignty. If God did not have a purpose for Satan, then Satan would not exist.
What possible reason would God allow Satan to exist? The sin, the evil, the wickedness, the destruction caused by his presence and activity. Why?
God allows Satan, and evil, to exist for a time. One reason is it gives the opportunity for God to reveal things about Himself He couldn’t otherwise.
Like what? Imagine if there was never any evil in existence… ever. No sin, no failure, no rebellion. There are aspects of God’s personality that would be forever hidden. Like His grace, mercy, forgiveness, restoration - all things He puts on display in the human race for the angels to see (see Ephesians 3:10, 1 Peter 1:12). Things about God that can only be displayed because He actually DID allow Satan and sin. Things God has allowed so that we may see His grace.
So Satan is allowed to do his thing. For now. And you can be sure God is still in control and using Satan to ultimately accomplish God’s purposes.