Consistency, quality and standardisation are the most important things here, not necessarily the same instructor. The supposed benefits of sticking with the same person all of the time are often over hyped and based on opinion!
The fact is that all of the students I have know (and there have been many) have had enjoyed much benefit from some variation in FI style and methodology. All FIs should be teaching the same syllabus but there is plenty of room for 'style' differences.
Imagine, you might be staying with one FI only because it makes you feel better... however, how do you know they are the best one for you if you don't try a few others? There may be much more compatible instructors waiting around the corner.
To say that one instructor is always best and will cost you less money overall is too simplistic and at best a myth.
Ultimately, you should do what you feel comfortable with.
Have fun!