It doesn't need a reboot. The comics have had the right idea by setting each storyline in direct continuity with the end of the TV Series, which technically saw its finale with the Return of the Joker movie. The Hush Beyond & 10,000 Clowns comic, JLB and Beyond 2.0 all succeeded in tying into the show's story, and even the latest Rebirth series is attempting to do the same as well.
It's because the Beyond TV series established such a strong roster of original foes for Terry, as well as a lot of prominent supporting characters in his school environment. You lose all of those things in a reboot, and it's no longer Batman Beyond.