This is a tricky, and somewhat subjective question to answer, and unfortunately, I don't have much more than anecdotal data.
Is fight effectiveness or personal defense an important goal for modern Capoeira?
Generally, no. Much like most modern martial arts from Tae Kwan Do to Kung Fu to Kickboxing, people primarily study Capoeira for the purpose of exercise and for learning new things. And most people who study it will never get into a fight and use it and if they did, they'd probably find themselves overwhelmed.
Can Capoeira be an effective fighting style?
Yes. Historically speaking, capoeiristras were considered to be on par with the Vale Tudo fighters of the day. Several MMA fighters today incorporate kicks from Capoeira in their fighting style. And if you try to pick a fight with a capoeiristra on the streets of Brazil, there's a good chance you're going to face a tough fight.
So, if Capoeira is effective, why does it seem so weak?
Well, first off, as I mentioned before, most people don't do martial arts to fight, so the vast majority of people you meet haven't trained to be good combatants. Secondly, most Capoeira schools don't train people to fight. The sparring is generally light to no contact with a large part of the prestige lying in setting up a situation where you show that you could strike someone with great force, or take them down, but you don't, merely counting coup on them. The rules of a polite fight forbid certain targets, which means that some of the defenses involve doing things like turning your back to an opponent or dropping to a crouch, because the other person won't attack you in your time of vulnerability because by doing so, they'd basically be saying that the only chance they have against you is a cheap shot. And that's not even getting into ritualized situations such as the chamadas, where you essentially invite an attack with the expectation being that instead you'll go through a ritualized set of motions rather than engage in attacking.
In short, typical Capoeira instruction does not involve an actual fight with full contact, and the rules (both formally and in the eyes of your peers) constrict what you can do, creating an unrealistic situation. And, well, you're not in there to win a fight, but rather to show your skill, and part of that actually involves avoiding shutting down the other person in the circle, because it's more impressive if they make a good showing as well.
Wait... I thought you were trying to say this can be effective?
Well, remember what I said about these rules being for a polite fight? Outside of a Capoeira school, you're not always in a polite fight. People might pull knives. They might try to hit "illegal" areas. And they might be bigger and stronger than you. In that case, you're expected to only follow the rules for as long as it's helping you. If you're up against someone who is actually spoiling for a fight, you give them one. You don't do acrobatics. You do an abbreviated ginga, if any at all. And you hit hard where it will hurt them the most. Also, as a number of people who've trained Capoeira for fun have learned when trying out their skills on the streets of Brazil, there are people who do this full contact, and find it funny to bounce your head against the cobblestones if you look like an easy mark.
Outside of that, Capoeira does require a large amount of physical conditioning, and you learn pretty quickly how to recover from a variety of ways to fall without rendering yourself immobile. While you are expected to not knock your opponent silly with a kick, you do learn to strike with full speed and force when you're against someone who you know can dodge. And you do learn to dodge on an instinctual level, and how to roll with a hit to avoid injury. With a little bit of cross-training to learn how to actually take a hit without stopping the game as everyone gives your opponent the side-eye for showing such lack of skill, the movements of Capoeira are indeed useful, although you're unlikely to use the acrobatics outside of recovering from losing your balance, and for intimidating opponents before a fight.
If I were to reach for an analogy, I'd say that Capoeira is a lot like Olympic fencing. Within a formalized arena, you get a chance to demonstrate your full skill. On the street, if you've only done the formalized version of it, it's not going to be super-effective, but there's a good chance you can hold your own against an untrained opponent because you are physically conditioned and have an idea of how to move your body. And with an additional bit of training, you can make it combat-effective.
Back to the subject of competition...
This is actually a fairly contentious topic for historical reasons. Back in the days when Capoeira was just becoming legal (because politicians realized it was actually something they could be proud of, and use as advertising), there were attempts to "legitimize" Capoeira by staging competitions. Since Capoeira's origins are on the streets, among the poor (and frankly, often the criminals), there was a pushback against this gentrification of the style, particularly since it codified a lot of the more formalized aspects of what you could or couldn't do in a fight. And, since it's so subjective, scoring is a tricky thing. A decent comparison would be breakdancing competitions on TV, particularly the ones where they're both sharing the same floor space. Whether one person outdances the other is subjective, and when you include improvisation based on what the other person is doing, your performance is dependent on them as well.
Add to that that such competitions were seen as a way to shift Capoeira to being a thing for rich people with paler skins, and you can see why the competitions are largely absent today.
