"Sync" is a word which generates plenty of emotion and opinion. Easily the most controversial feature of modern DJing, people argue it's use means the person is not a DJ. It certainly removes a major skill element from DJing, namely beat-matching, however it also provides the DJ with a lot more time and control to do more complex techniques. Here are a few uses of sync that don't summon DJ Satan to drag you to hell:
1. Allows Massive BPM Changes During a Mix
This is one of the only times I use sync. I like beatmatching, it's a big part of the fun and challenge, but I have my limit of skill. When I'm mixing two tracks with largely different BPMs, you may want to mix them in at one BPM and mix out in another.
For example, let's use a house song, 124bpm, and a trap remix of that song, 70bpm, as an example. I am starting my set at 70bpm and playing the song out. As this trap song, is nearing it's end, I want to change the vibes to the house song. I need these beats to match, so I bump the house song up to 140bpm.
The two songs are now playing together at 70/140bpm. This is where you hit sync. Why? Because you can now gradually slow the tracks to 124bpm and you only need to use one fader.
If the tracks weren't sync'ed, they would not go down at the same rate (pitch faders work on a % scale so bringing both faders down the same distance won't make them the same tempo).
Now both songs are at 124bpm and the trap song can be mixed out.
2. Dealing with Samples
Most DJs will agree that keeping two tracks in sync is a hard job by itself. If a DJ wants to incorporate samples into their mix on top of the tracks they are beatmatching, there is a lot to focus on. This is why sync has been a major development for creative DJs.
If you consider Ableton performers, all their loops are synced to a master tempo, they don't get given as much grief. Incorporating samples into one's set is much the same. It really just has to be automatically sync'ed. This kind of performance is judged on the live production element as opposed to the turntable skills.
The advent of stems has provided more justification for sync, where tracks are split into four sections. Unless you want to beatmatch 8 tracks for every mix, sync will do just fine. Again it is the performance and creative aspect that these DJs are providing, not traditional skills.
3. Fixing a Bad Mix
Train-wreck imminent, your reputation about to fall. Dancefloor soon to turn into a barren wasteland. Do you get over your moral obligation against sync and correct your mistake?
I don't see any issue in fixing a bad mix with sync. I have done that twice live in my history. It really saved the show. Call it a repair tool, a tool that stops you getting boo'ed off stage.
Let's face it, if you use sync in this sense, you know you need to beatmatch, and using sync is not ideal. But so much happens in a booth, some things you can't control. For example, the last time I recovered a mix with sync was when I was trying to fend away some drunk guy whilst beatmatching.
Your mix gets interrupted. It's not your fault do your best to fix it and move on. Worst case is not hitting a button that is unpopular. Worst case is destroying your set with a train-wreck.