Vocal coach Molly Webb also advises a movable larynx, and discusses the possible origins of the 'stable larynx' training. Quoting her from her article:

As long as you only raise or lower the larynx so that you don't feel your throat or experience strain or fatigue, what you're doing is fine. In fact, as a session singer (or stunt singer, as I call it), I have to do sometimes over-do this to blend with all kinds of voices and styles for recording. Changing the level of the larynx is a way to create more tone colors than usual. Various character roles in musical theater can require more unusual tone choices, too.

In fact, it's not just slight raising and lowering that we need to allow. To accomplish higher notes, the thyroid cartilage which comprises the largest part of the larynx needs to be free to tilt in your neck! Tension in and around the larynx from trying to keep the Adam's apple stationary can interfere with these movements. What's the Adam's apple you say? Officially named the larygeal prominence, it's the pointy front of the thyroid cartilage that sticks out as a bump right in the middle of the neck. It's very noticeable in a man but a woman has a small one, too. I like to call it 'Eve's apple'! The front end of the vocal cords are attached directly behind it.

However, and it's a great big 'however', you should not lower or raise your larynx to the point that you become aware of it. That will give you vocal problems. Most contemporary genre singing really should be in what Lisa Popiel would call #3, the middle position, with the larynx freely and comfortably floating and tilting in the throat.

What can you do if your Adam's apple and larynx are too stationary, not free to move?

What can you do if you are raising or lowering your voice box (larynx) too much?

Learning to PULL instead of PUSH your voice, as taught in my Power, Path & Performance method, is the best way I've found to protect your delicate and precious vocal instrument, and will help you immensely. This pulling instead of pushing for sound, among other things, allows the larynx to determine it's best position with no outside interference. Also...

Here is a very effective exercise I adapted for my students from yet another great voice teacher, the late Jeannie Deva:

Lightly touch your adam's apple with the tips of your fingers. Feel for it in the middle of the front of your neck; and ladies it will just be a little bump. Again, this is where the vocal cords are attached at one end, inside the thyroid cartilage. Now, just let your fingers be "brain flashlights" and make a mental intention not to tense the area under your fingers as you sing. It's an amazing tactic when your larynx tries to lift for high notes. Notice how high notes, including higher middle voice notes, just float out almost effortlessly instead of strain!

For low notes, try this to keep your larynx from lowering too much: Stand tall and put your hand on your sternum and try to pull your voice from there. It will help your lower notes sound rich, not hooty, and will feel better, too. Don't bend over or down to get the notes. Be aware of the vibration and keep your chest open.

These are great voice teachers I've named in this post. It can get confusing, I know, when experts differ. All I can be sure of is what I've experienced that WORKS, and this should be your criteria, too. From my experience, I say mostly just keep your larynx happily floating, actually rocking a bit, in the center of your neck. Allowing it the freedom to move slightly lower or higher should give your voice a wider range without strain!