Mainly my skepticism is pretty much about having to choose whether to move or not.
This is actually what I like about it the most. The player always has the option of rolling an action die and a move die. Choosing not to roll one of them is a chance the player takes in order to get the initiative advantage (not advantage in the 5e meaning of advantage of course....)
Instead being locked into non-moving is IMHO potentially a much worse situation for melee characters, while it is almost always irrelevant for ranged characters and spellcasters.
My response to this is that 1) It makes perfect sense from a realism point of view. It should be easier (though not guaranteed) for someone rapidly shooting arrows to stand and shoot before someone else can run across the room and hit with a weapon.
and 2) Also, given that the ranged character consciously forgoes the move die, and thus the chance to move in that round, if an enemy were to shaddowstep, teleport, dash, sneak, become visible, or whatever, within melee range of them unexpectedly, they are now stuck standing there that round, and possibly through the enemies attack in the next round should they lose initiative to a creature that does now have incentive to forgo the move die since they have a vulnerable enemy in melee range. How devastating would it be for a character that specifically avoids melee combat to face a killing machine toe-to-toe for 2 rounds? That would be incentive for them to keep their options open and roll the move die just in case.
Also, a lot of the complaints I see are phrased such that melee fighters will "always act last", which is not true. Not only will chance still play a roll, but there are plenty of times where it is tactically reasonable for a fighter to forgo movement. If they are guarding a door or corridor, the resolve to stay in that spot provides a tactical advantage against anyone trying to get past them.
I think people who treat combat with the minimum commitment (simple TotM with minimal description of tactically useful elements of the battlefield, simple one roll per side initiative) are not the kind of players who will see any value in an initiative system like this. And that is of course a valid option for their game if that is enough for them. If you care about a more realistic representation of the chaos and unpredictability of combat, gaming groups may want to consider a system like this.