There are plenty of players that bring the ball up the court that don't have great ball handling skills.

Plenty of teams let their SG or SF bring the ball up and those players don't have supreme ball handling skills. Looks at James Harden or even LeBron James. They frequently bring the ball up the floor and I wouldn't put them in the elite dribble category. Of course they aren't being defended by other quick PGs and their other skills supremely outshine any problems handling the ball.