Why do some doctors use the tissue expander for the hairline lowering procedure while others do not?

Doctors have their unique technique and experience which may differ with another doctor.  Patients also have their unique issues and the treatment options may vary between patients.  There are many ways to do the same thing.

3
cms of lowering (over an inch) is not necessarily an “only” for if your scalp
is tight, meaning not very elastic, it may not be possible, even with a surgeon
such as myself who performs 3 to 4 of these hairline advancement surgeries
monthly, to get this much advancement. The expander can increase the
amount of advancement. I evaluate patients like yourself with a video in
which you demonstrate how much laxity your scalp has.

It depends on how much the doctor is planing to lower the hair line and also the degree of elasticity of tour forehead skin.  For tighter scalps a tissue expander may be necessary.

The tightness of your scalp will determine if your hairline can be successfully lowered to meet your expectations without expansion. A patient who wants to lower the hairline 3.0cm must have a moderately loose scalp. This is a procedure that we described many years ago; I've seen many patients  who were told that expansion was not necessary and then came to me dissatisfied with their result.

The recommendation for use of a tissue expander prior to a hairline lowering  operation is a matter of clinical judgement related to factors of scalp laxity, hairline shape, and the distance the hairline is to be lowered. 3 cm of lowering would demand good scalp laxity, good quality hair at the existing hairline, and similar shapes of the existing hairline and the desired lower one. Also the configuration of the temple hair has to be taken into consideration. It is preferable to be able to perform the operation with one stage. Certainly there is less tension on the suture line when the scalp has been expanded.