Can teaching help one's studies? Most of the questions about teaching assistantship portray TA'ing as a waste of time that only damages research. Although I am not TA'ing this year I consider applying for a TA position next year, because I feel I kind of missing it and it actually helps me to focus on my research.

Are there any clear benefits of TA'ing for one's studies and research?
Of course, it depends on how much teaching you would be doing, and how many hours a week it would take you, but generally, I would consider the following pros/cons points: 

Pros:


Teaching might allow you to meet other people than those you are doing research with, and interaction with different people can be useful in terms of research (for instance, you can find a nice collaboration idea with a prof or another TA). 
Teaching brings more immediate rewards (positive and negative) than research. When I was doing my PhD, I was also teaching (about 60 hours per year), and sometimes, when I was stuck with some research problems, it was a nice feeling to interact with students and to feel "productive". 
Teaching is a good training to clearly explain ideas and concepts, which an important skill to write good papers. 
Teaching provides you a different activity aside from research, and can help you focus (as you said yourself). 
Teaching is good on a CV, and if you consider applying at some point to a lectureship/professorship position, then having done some teaching during your PhD can allow you to do some more research-oriented postdocs after (and thus get potentially more papers), so it's somehow a good time investment to do it when you're not expected to produce a huge amount of papers. 


Cons:


Teaching takes some time, especially if you are teaching in a field where you are not an expert. 
The downside of the immediate rewards is that sometimes, you can get frustrated because of the teaching, and that can have an impact on your research production. 


In conclusion, I would say that being a TA has really clear and acknowledged benefits, as long as it does not take too much time on the research activity (I would say no more than a day per week during the official periods of teaching).