Scenario 1:
We're diving in Greece where the dives were conducted by a Swedish PADI instructor. In between dives we just make idle chat on all things diving and the topic of safety stops comes up. I mention that we do most of our safety stops for 3 minutes at 5m because that's what our computers (Suunto) prompts us to do even though we have been trained to stop for 1 minute at 3m. He then launches into a scathing attack on our training because "you actually off gas quicker at 5m than at 3m"
Now I'm sure there's room for debate on what depth is better for a safety stop but that you'd off gas quicker at 5m than you would at 3m is patently untrue and only a complete fool would use such a bull**** argument to attack another agency's training.
Actually, it depends on your decompression model. You off gas dissolved gases fastest when at the highest gradient (shallow stop), but if you look at any of the bubble-models (RGBM, VPM/B) they want to keep you deeper. The dissolved-gas model takes you to the shallowest depth you can go to without bubbles forming, and holds you there while you off gas. The bubble models assume that micro-bubbles are continually forming and redissolving in your blood (and other tissues) during your ascent. By keeping you deeper, you keep these bubbles smaller, where they aren't going to cause problems.
Any technical diver would scoff at the notion of doing their deco at the shallowest depth possible.
So I wouldn't necessarily agree that you "off gas quicker at 5m than at 3m", but it is certainly a better place to be doing your off gassing. A deeper stop (which controls microbubble formation better) is going to work to prevent Type II DCS (neurological), whereas the shallower stop is going to work to prevent Type I DCS (muscular, joints). I'd rather take a Type I hit over a Type II any day, so I'd rather do my stops deeper (even if I had do keep them shorter as a result).
Regarding the necessity of safety-stops, you need to do them with EACH ascent. Certainly they aren't required, and if conditions dictate that it isn't safe to remain in the water (being circled by a great-white shark, being blown out to sea, low on gas), you should skip it and get out (you can fix bent, but you can't fix drowned). Consider this case -- you complete your safety stop and drop something, you bounce back down to 20m to pick it up. Can you skip your safety stop on this second ascent because you've already off gassed? No! One of the purposes of the safety stop is to let microbubbles in your blood complete their circulation and get trapped in your lung tissue where they will not cause DCS symptoms when they expand further during your ascent to the surface. When you drop back down, you compress these trapped bubbles until they are small enough to leave your lungs and go back into circulation. A slow (10m/minute) ascent rate and a second safety stop is just as important this time as it was the first time, to get these now-expanding bubbles to "trap" in your lungs again, rather than somewhere else in your body.
Is buddy-separation an emergency warranting skipping your safety stop? In my opinion, no, unless where is reason to believe that your buddy is going to need your assistance getting to or once on the surface.