No. As you correctly point out, competition isn't training. An individual can compete and not learn from it, not make useful adjustments. In that case, they don't benefit from it, so it won't improve their skill.
What? That's rubbish. If you train in BJJ 3 to 4 times per week diligently and compete 2 or 3 times per year regularly, you may not be the next coming of Rickson Gracie, but you will certainly become skilled enough to earn a purple belt. Absent injury or illness, you just simply can't fail. Though there may be some exceptions to this rule.
It's like learning to drive. Driving is a difficult and complex task. But just about everyone learns it. They spend some time in focused training, where they are expected to also apply the skills under the watchful eye of a coach. And then off they go. Bad drivers who, hopefully, through application, will become good drivers.
It will tend to improve the group, though, in two ways. Firstly, with folks competing, they have more feedback to improve the system. BJJ is an excellent case in point for this. Secondly, folks who aren't good in competition won't tend to stick around (there are exceptions), so the group's overall skill level improves somewhat by attrition. I assume (though can't prove) this latter is a minor effect in most cases, though it seems likely the "harder" the competition, the more of this effect there will be.
Also rubbish. There are all kinds of people who HATE competing who do it because they know how important it is to their development. There are people who compete and lose every time. Not everyone is a phenom, and there are sharks in every school. You are articulating an argument against competition based on, I believe, your own hang ups and insecurity about losing. The thing about a performance based art like boxing, BJJ, MMA, or any of the numerous others, is that in order to improve you have to get over looking foolish or feeling embarrassed because you suck. Everyone sucks relative to someone else. The only way to get better is to lose less often.
The group gets better because the group supports the individuals.
The above rationalization is a perfect example of the kind of rationalization I mentioned to
@skribs in another thread when he talked about training in BJJ. There are a lot of people who are worried about looking foolish who can't get over that ego, and so they create fiction like yours above to rationalize their decisions. So, to be clear, the reason people leave is because they are not resilient enough to do something that is actually hard to do, where they may not see immediate results. But that's not a training model issue. That's a resilience issue, and something we really need to address in our culture, where folks are told all the time that they can lose weight by taking a pill, or gain lean muscle by strapping on some electrodes.