The most important part of jiu-jitsu is the constant testing of ability in full resistance situations. The majority of this is done in sparring during training but competition also plays a big part.
I think, if nothing else, everyone should compete at least once. I, and many others, love competing, so if someone doesn't give it a try I think they could be missing out on something which will make jiu-jitsu even better for them. Now, like anything, lots of people won't like the experience. Competition is tough, can be stressful (if you get stressed I guess, I've never felt stressed about anything), you'll feel the effects of adrenaline, possibly nerves and if you lose everyone gets to see it. Personally, I don't really think these are reasons not to compete... they are problems to overcome and doing so will help to improve your jiu-jitsu. But hey, if you try it and don't enjoy it there is no reason to force yourself into it and maybe destroy your enjoyment of jiu-jitsu as a whole.
So, I don't think it's wrong that an individual doesn't compete... what I do think is pretty lame are entire clubs which don't compete, or have very few active competitors, or none of the instructors ever compete. Without students and instructors stepping outside the academy to compete, it's impossible to judge the club's overall level of ability... does each level of belt at your academy stand up to those from other academies? Can your academy compete against the rest? Are the students well rounded or is there an area where lots of people struggle? These are all questions which regular competition will answer. Also, without a large number of students competing regularly the sparring in training is likely to lose it's edge and become too far removed from a proper test of ability.
As an instructor I love watching students compete because it is the ultimate validation of everything I do. If they can use the jiu-jitsu I have taught them to beat people who are fighting 100% to stop them, what more can I ask for? It shows that not only can I pass on techniques from my instructors but I can develop people into actual fighters. This is why it's important for a club to have a large number of competitors too. Individuals can win fights and even whole competitions through athleticism or just toughness, but if a team produces multiple winners then they definitely have a high level of instruction.
Having said that, it's important to note that winning can't be seen as the only worthwhile goal of competing. When stepping up to fight, everyone should always believe they can win, but being realistic there are plenty of cases when it's highly unlikely. However, if you start to focus too much on gold being the only reason to fight it quickly makes people only want to fight if they can train every day, do extra strength & conditioning work and cut down to the lowest possible weight class... the real reason for competing should be to get out there and test your jiu-jitsu. You can do stuff in the academy, but can you do it under real pressure? It's easy to go for something in training knowing that if you fail and it goes wrong, it doesn't really matter, but in competition if you fail with one technique it could mean you lose the fight. That's where the real test is.
I wrote about excuses from people who say they are going to start training but never do... competition is probably the thing which produces the most excuses from those who do. Excuses not to compete; "I can't make the weight I want to fight at", "I haven't trained much the last few weeks", "I've only just been promoted" etc... I've heard them all and more numerous times. Simply put, competition isn't fair and it isn't meant to be. Even with the belt divisions in jiu-jitsu there are massive disparities in skill level within each belt, some people train once or twice a week whereas others train once or twice a day, some people have a lifetime of athletic training while others might have started jiu-jitsu totally out of shape... if you want a fair fight (and most people probably want a fight in their favour if they're honest) then competition is not the place to find it, but it's also not the point. Competition is facing the unknown and seeing how you fare. You put everything on the line and win or lose it's the most honest test of your skills possible.
The second part where excuses come in to competition are after losses. People say "I didn't get any sleep the night before", "I hurt my knee two days ago", "I didn't drink enough after my first fight", "The ref screwed me over" etc... and although things like that no doubt contribute to the result, it is the wrong thing to focus on afterwards. Everyone has those problems, including division winners and medallists. If you allow yourself to blame outside factors then it's easy to start not caring about winning or losing. All that matters is what happens during each fight and what you can learn from it.
So what can you learn from competition? Mainly, can you fight in a high pressure environment and use your skills against someone who is resisting to the maximum of their ability. But there is more than that... are you able to remain calm? Can you deal with the adrenaline which competition causes? Your cardio might be good in the academy but can it get you through multiple competition fights? Then there are smaller things; competition is a good place to find technical areas you struggle with. It's easy to not realise certain things you aren't good at in training. You might get caught in a submission you had never learnt an escape for, or you might find out you're not as good at escaping side control as you thought. All these are issues you can go back to your instructor and work on in order to improve your jiu-jitsu ability.
"It's not the winning that matters, it's taking part" is something I'll never tell anyone and never believe. Winning does matter, the point of competition is to try to win. It's just not the only thing which is important, and it doesn't mean that if you lose you shouldn't be able to enjoy the experience. If winning didn't matter, competition wouldn't matter. Fight to win but don't discount the experience if you lose...
...and there will be losses. If you compete then at some point you will lose. It might be a clear loss through being submitted, or by the closest of margins, or even a contested loss due to poor reffing, but regardless of why and how, you will lose. The fear of losing is probably the biggest reason that a lot of people don't ever compete but I think it's a silly reason not to. Just like tapping is part of training jiu-jitsu, losing is a part of competing, you just have to accept it. Now, that doesn't mean you shouldn't care about losing, I hate losing. But a loss isn't just an end to a competition, it's another experience which you can learn from and improve your jiu-jitsu... and sometimes even a loss where you get dominated can have positives; if you managed to not get tapped and escaped bad positions against a much superior competitor then it bodes well for future competitions.
So get out there and compete. Test the skills you spend so much time and effort on learning. If you really don't like it then don't force yourself, but please try it at least once!