So like you can see in the Title how you would rewrite GT for make it Good ? What you will change/add/remove ?
Arc search of the Black Star Dragon Ball + Arc Bebi:
First portion of the Show the adventure and fetch of the Dragon Ball. Ok let's have the son of katats had created a first set of Dragon Ball before he split into Piccolo Daimao & Kami-Sama but the set wouldn't have impact on earth whatsoever.
Since there is no repercution and thus urgency Goku & Vegeta said that the kids will fetch them, like that this will be great opportunity for them to gain their own experience through adventure.
The people select for this task would be Uub, Trunks, Goten and Pan (I want to add also Marron & Bra but I don't think everyone would agree) everything happen similarly to the serie but instead Legdic join the gang and become Uub rival.
They succeed their task but Bebi come into play and instead of choosing Vegeta he Choose Gohan (For a more emphasis drama between Gohan and Goku and Pan) There Vegeta and Goku have great difficulty against a powerful Bebi Gohan.
Here we can have Piccolo die by the Hand of Bebi Gohan (who also thanks to Gohan brain come up with way to increase the half Saiyan body strenght) imagine the cheer drama Gohan killing his former teacher and dad by interim.
After Bebi defeat by a collegial effort of Vegeta and Goku everything is back to normal minus Piccolo who choose to stay dead and watch over Hell.
Arc Rise of Hell and Super A-17:
For the second great arc instead of this Super A-17 being created from two A-17. I choose Ozotto has the one who mess with Hell (Ozotto is a shapeshifter Majin dubbed also as Super Monster) so Imagine him being one pain in ass with manipulation and deception, also let's give him a power on par to Majuub and both Vegeta/Goku SSJ4.
Here with all the hell resident coming to play on earth I'll reintroduce A-17 and A-18 and make them undergoes a power up thanks to Bulma and Gohan studdies on the Brutz Ray giving to their power infinite cells higher specs. So A-17 will have the design of Super A-17 but here served to beat people as powerful as Cell or Freeza, let's not forget A-18 who would become Super A-18.
All earthling would have their great moment and mostly Yamcha dealing with Nappa and Gero.
And I'll have Pan and Bra goes Super Saiyan as well.
Arc of the Shadow Dragons:
For the last arc I will not change much perhaps just change several design of Shadow Dragons and make them more Badass. And instead of Gogeta SSJ4 I'll have Vegeto SSJ4. Perhaps why not also move the battle on more than one planet and scater the Shadow Dragon around the Universe.
With Yi Xing Long being on New Namek (Ding Dong you can see it coming the Power Up of the Shadow Dragon thanks to the Namekian Dragon Balls).
As for the ending Goku who died saving the Universe with a Universal Genkidama is brought back to life once more but is taken to the Ryushinkai with Porunga and Shenron. The Kaioshin finishing with a ligne that the Era of the DRAGON BALLS have ended and Vegeta have the final sentence with let's face a new era without them farewell Son Goku.