They build authority and hone writing skills
There are many benefits from doing this. Perhaps the main one is that they can truly impress your followers. People can tell that you know your stuff because of what you say, not just because of what you share. So they help build your authority quickly.
Then there's the fact that the limited space you have to use for this requires discipline. You have to cut right back to the central point. So it's a great writing exercise.
If you can get into the habit of doing this, all the better. Practice makes perfect, as they say. Do this enough and you'll start to find yourself thinking up pithy one liners and insights in your spare time. Then when you next log into Twitter, you'll probably have a few up your sleeve all ready to post.
Can be used in other media
And you should save them on a file because you can use these tips and tricks elsewhere. A compilation of them on a specific subject makes a great blog post. They can also be used in other online and offline media.
Speeches in particular are a great place for them. As well as live speeches at networking events, etc, you can rattle them off in front of a video camera and upload them to YouTube.
Speaking to camera for a couple of minutes is an oft-used approach of course. So you'll be up against a lot of competition. But you'll be jamming the same number of good insights into a two minuter that you would normally put into one three times as long. And because you're relating a bunch of useful insights that are crystallized and powerful, you'll speak confidently and convincingly. So your content will stand out amongst all the rambling, low quality stuff and attract more engagement as a result.
They entail a possible risk
There is a potential downside to this overall approach, however. And that is that you might be giving away some of your best lines on Twitter and other social sites. Because they're concentrated and powerful, other people might start to use them, claiming them as their own.
That said, in the same way that Twitter is making such plagiarism easier, it's also supplying you with a time stamp that shows you created the quote -- well, at least for a while until Twitter dumps your data. That's why you should also share it on another social network, and include it on your blog.
If you are worried about this possibility, then it's advisable to keep your very best short insights to yourself. Maybe you can save them all up, then put them in a book?