TL;DR version of the answer:
If you are capable of creating a full language and you need a new language as a part of other form of art / storytelling / fiction (not as an end in itself), it makes no sense to do a full language. It's wiser to use your time to fake it well, given that you know how a new language should be, and use the saved time to specifically focus on what would have been side benefits on a full fledged language. It only makes sense as a means of expression for its creator, valve of some sort, or if it's an end in itself.
I like the other answers, they enter the details of the 'why', analyzing the objectives, effects and results of such process, and the objective benefit it could bring into story-making. Many of them explain perfectly valid reasons.
It kind of depicts the writers as entrepreneurs, with plans for everything, win-loss balances for their actions and cost-estimations for their time, or caring about the cost of opportunity on investing time in give depth to one aspect of their work.
I think maybe a plausible answer is the other way around. It may be a symptom for a vocational writer, the opposite of money driven people who would create just nice sounding phrases, and strange looking symbols, (i.e. efficient investment of time) and be contempt with it (it has more or less the same effect on the general audience). So I'll try to address some of your questions from the creative standpoint:
Considering both type of writers with the same intelligence and knowledge level, both with the skill and understanding of linguistics deep enough to create such thing from the start, one kind vocational and the other 'entrepreneurial' (for my lacking for a better word):
Why do storymakers and worldbuilders put this time and effort into making new languages?
Surely not because someone with the skills to create a new language couldn't arrange some sounds and place some crafted symbols in consistent enough ways that in the end, the audience feels like there is a complete alien language behind. The entrepreneurial writer (or the vocational pressured by uncaring publishers, equal in this case) will patch up something smartly, and have a happy audience nevertheless. Not many will care what hardcore 'freaks' like to brag they can squabble in, or talk about in forums that 99% of their audience won't even know exists.
Why then put the effort into something that is wholly behind the scenes?
Other answers point out that it may help bring depth, or attract hardcore fans, or develop a better story altogether.
That makes sense, from the perspective of writers that pursue completeness or depth in itself, but from a (vocational) artists standpoint, not so much. Their point of view is from what they want to express, not what they want others to perceive. (Why would not make sense if what you care about is what others perceive is discussed more deeply in the answer to the next question).
Those storymakers and worldbuildes ALREADY have that language in mind, like working on it on their free time, and happen to feel the urge to either share it with the rest of their work or it inspires the rest of their world.
I'm basing this answer in the fact that I myself feel similar urges and like 'daydreaming' in similar ways. If I ever make a game, or write a novel, or make a film, it won't surely be because I want to do something people like and get recognition, or to attract hardcore fans, or to make money with merchandising in the long term. That may be a welcome side-effect, but it won't be the WHY. That's has nothing to do with what a (truly) creative person thinks about when making something. It's the other way around. They have inner worlds, and feel the urge to 'solidify' them into something. It's more of a mind relief, or and act of conservation of ideas. I myself, feel the urge to at least write down or sketch most of the creative ideas I come up with. It's hard to let them go knowing that doing so may incur in forgetting them completely, and so, maybe losing them. So it's either to create a tangible version of your inner world, or risking not thinking about it for enough time until it's forgotten. The decision may be based upon your perceived worth of the idea and your skills to create any form of representation of abstract thoughts.
Some will feel relieved and don't do anything else, others, completist enough, may refine such sketches into something more. After completion, some of the creative people is confident or bold enough to release such creations into the wild. Some get recognition, may even find out that their success was based on the sincerity of the representation of their inner worlds, breaking what's established without much shame. Some end up with things that are already common, but is possible that it feels new to some critics and audiences. It's even possible that it has nothing so original about it, we are mostly under the same conditions and sharing environment, after all, so it's perfectly natural that the same ideas evolve simultaneously and from distant origins, isolated or not.
What really are the major benefits of having a new language?
From the audience and money driven writer point of view:
Asides from less work creating social and cultural background for the species involved, not much. If the part of the time saved is put in designing better cultural backgrounds and social structures for your species involved, or more original sounds and alphabets; the positive side effects are greatly diminished by the cost of creating something complete rather than just a facade. In many aspects you could create far better results with superficial patches if you invest half the time it would take to build the real thing (almost a must in most aspects of the cinematographic industry, where the creation process involves too many paychecks to be done the way the director/writer wishes it'd be really done). I don't think it's hard to extrapolate this to many of the aspects of the creative process.
Then, once again, the major benefit might be that the creator does not have to be constantly thinking about some thing that he/she likes and will be lost if forgotten. And even more important, once 'solidified', you can free your mind and expand upon the idea, add detail, explore and tweak it to let it be more than it could possibly had been holding it all in your head at the same time. Musicians do it, writers do it, ... Is a must to succeed? Probably not. So the major benefit for having a new language might be, simply, that the creator is happier.
What is the explanation for why it's worth the time to create?
Generally, it is not economically worth the time to be any kind of artist or create any kind of thing. It's a ticket draw. It will be worth a lot it if it's what the audience fixates upon, and if they like it so much after they notice. Or it can be ignored. Or disliked. But as any ticket draw, for every successful artist there will be many more who have put exactly if not more effort and won't succeed. I don't have the numbers, but you can easily see that dividing the collective benefit any of this could bring (mostly will be from the successful artists) to the collective effort put in it (where non successful people outshine the others) won't add up to any economical worth.
On the other hand, other kinds of 'worths', like the ones mentioned before, less tangible but providing happiness to the one that invests the time and effort, may be unquantifiable. I'm quite sure they wouldn't be doing it if it was not for those other kinds of worth. They'd be earning a paycheck doing some other thing that makes them equally not happy but brings more money and is more reliable, or investing in other more noticeable aspects of their novels or whatever. People doesn't do theses kind of things for money. (Creating intangible depth, that is. People will surely write what is easy to sell without liking it!)
I tried to answer in the most general way, as I felt that the answer to the tangible benefits of an invented language were already pretty well exposed on other answers, but as your question incurred in the 'WHY', I felt like there was no good answer exploring the reasons behind all the dubiously economically worth forms of art or creation, which I think this is a case of.
The answer in short terms:
Because whoever creates something does not want it to be just an idea in their head.
Finally, I'd like to add a reason some people do things: They think it's soo damn cool. It could answer to 'why?' too, though it really is just a simplification of the above reasons.