Adobe Audition's "Delete Silence" Feature for Premiere Pro.
Just like Adobe Audition's "Delete Silence" feature, but in Premiere Pro. The only difference is that the audio will also ripple cut it's linked video.
With an unbelievable amount of YouTubers having to manually edit videos like this, and with Adobe coming out with seemingly more taxing features like "Smart Edit" and "Scene Edit Detection", I think the is wholly possible and will absolutely be heavily utilized.
Edit: A really necessary aspect to this would be that the cuts need to be accessible to the user, much like they are with "Scene Edit Detection".
Alexandre Fauchard commented
You can also try our Premiere Pro extension: https://www.autocut.fr/en/
The extension does exactly that and there is a 14-day free trial.
Paul Murphy commented
Here's a way to split your video into subclips that exclude any silent pauses - no plugins required: https://youtu.be/wtmZnBpaRpI
Kevin Monahan commented
This is a good one for vloggers, I think.