On the Oscar, CJ does almost nothing. On the OBIR though, CJ3 is noticeable. What CJ3 does for the OBIR is that it keeps your shots tighter together: the bullets coming out just a bit sooner means that spread has less time to accumulate, since spread is not applied instantly/evenly. The end result is that your second and third rounds in a burst are more true to the center of your aim, actually increasing mid-burst accuracy.
For an example, look at CJ3 on other weapons, such as the N-Tec. If you fire the gun full-auto, you'll notice that CJ3 allows you to get a bit more accuracy on the second and third rounds fired, almost enabling a sort of burst-fire strategy. That's for that very same reason: you're firing the next bullet before the spread has completely applied. This is noticeable with the OBIR if you pay close attention, and it actually makes a large difference at longer ranges.
Now, CJ as a whole is seen as a TTK-lowering mod, so when people see it not lowering TTK on burst rifles, they think it's pointless. It's odd that CJ affects burst accuracy in burst guns instead of TTK, but in my opinion it is a very important effect. The issue of CJ not having a downside on burst rifles remains, but rest assured that it does currently make them stronger. In fact, I refuse to run OBIR without CJ - IR is nice and all, but if I miss a bullet because of the burst spread, I've gained nothing with the increased range.
If this mid-burst speed/accuracy change stayed alongside a TTK drop, I wouldn't mind (well, except for OBIR already two-shotting fragile at 0.45s, and lowered burst interval makes that even quicker), but please don't remove the mid-burst fire interval buff. If it were ever changed, I'd still want some way to have that burst modifier, since I really do find it so useful.
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EDIT: To be more clear, I want to respond to these two suggestions:
1. Decrease the time between bursts, but slightly increase fire interval.
This would completely destroy what CJ is currently good for. I thoroughly disagree with this change, unless the fire interval buff is put onto another mod (unique to bursts or not).
2. Decrease the time between bursts, but slightly increase per shot modifier.
This makes sense in keeping with CJ's theme, but this also destroys the upside of CJ that I've explained. Again, I either disagree or want the fire interval change on a different mod.