I've done it both ways and prefer the "instructor "du jour" system. I
got my Airplane Single Engine Land rating with a single instructor from
start to finish. Then, added the glider rating "the other way".

Different instructors stress different points so, in the long run,
you'll get a broader education. There are two potential downsides.
The first is that unless all of the instructors communicate well, it may
take longer to complete the training due to excess repetition.
The second is that the student will get conflicting information that may
be different to sort out.

Some prefer one method, some the other.

Tony, LsS6-b "6N"