This is probably a popular question right now because of the success Jon Rahm is having right now.
The biggest advantage I see with a shorter backswing is you can usually gain more control. I know Rahm is a big hitter, but he is more of an outlier, not the norm. Most of your big hitters get the club parallel to ground at the top of the backswing, or close to it. Rahm barely gets his left arm parallel to the ground. Generally the longer the clubhead has to travel through the air, the more time it has to pickup speed.
If you are looking to shorten your swing you will probably need some drills to do so.
I would suggest starting with hip to hip swings. The club does not get much higher than hip high. Once you feel comfortable with that then start making L to L swings. Your lead arm will get parallel to the ground on the backswing and shaft will be 90 degrees to lead arm, which creates the letter L. Create the Letter L on your follow through also.
From there start working on what feels like a 3/4 swing. Make sure you understand the difference between how your full swing feels and a 3/4 version of it. In the beginning you do not need to be hitting balls. Get in front of a mirror so you can see the positions, and then start putting a feel to those positions.