I can see some of the benefits. A lot of time would be saved at the beginning of a year that is usually used as 'getting to know you' time. Obviously it is very important to connect to your students on a personal level and this cannot be done overnight. You would also have a good idea of the different ways that each student learns. At the start of the year time needs to be set aside for pre-assessing students for specific skills and abilities. This could be heavily reduced if you had a good idea of where they were coming from. The dynamic of the class as a collective and what they do and don't respond well to is another thing that takes time. If you have the same students from the previous year you can get straight into the curriculum and not have to worry about a lot of the aforementioned. Time is at such a premium in our crowded curriculums and this could be one way of finding some more.
A situation where it may not be beneficial for students to have the same teacher for consecutive years could be if the student and teacher do not have a strong relationship. Perhaps the teacher is ineffective, perhaps the two personalities don't mix, perhaps there are other reasons. There are many occasions where people work with each other purely on a professional level without any social connection and this may also happen in the classroom. Although, in Primary School especially, I think this would very difficult. There would need to be a lot of trust between the teacher-principal-parent triangle for things to work in this situation.
In progressive systems of education (eg. Finland) teachers regularly have their students for more than one year. I am sure this is practised in quite a few systems around the world but I hardly hear of it - unless a school is under-staffed and teachers are forced to combine classes. I can't think of any International Schools that follow this system. I wonder if this model is considered in many schools? Is it too difficult to manage? Proven to be ineffective?
Next year I have a teacher joining my team that has taught in the grade below me this year. It is possible that she'll have some of the same students in her class and I'll be interested to hear her opinions on this subject.