You trade the pick because 1) you are already loaded at that position, 2) you can get a top 10 player in the league for the pick, 3) your team is a piece or two away from being a true title contender, 4) Fultz doesnt fit the current team’s timeline for success.
If you keep the pick and take Fultz he is likely your backup starting the season, as it would be crazy to start him next to Thomas, and you arent going to have the second leading scorer in the league being your 6th man. A backcourt of Thomas and Avery makes sense, now and in the future, as each makes up for the other’s weakness. What Boston needs is another big and/or a starting caliber sf. You could possibly sign Hayward, but why not also try to trade for Butler or Cousins in the process. Running out a lineup of Thomas, Butler, Hayward, Crowder, and Horford, with Bradley, Smart, and brown off the bench is good enough up front and off the bench to compete against the Cavs and at least push the Warriors. Having Fultz come off the bench, doesn't do much for the teams success now, but does help the team 5 years from now.