There is no time in life where you will reliably know both legs can stand at an ideal distance next to each other in order to squat in the conventional sense.
You don't know you'll always have both legs.
You don't know you'll always have both legs uninjured and rested.
You'll never encounter a surface where both legs can handle the load perfectly symmetrically.
The majority of skeletal body types are not ideal for conventional squat; and most instructors don't know about this. They teach for one set of levers, theirs. I have encountered even very intelligent and educated strength coaches who know absolutely nothing about anthropometry.
Especially with this hatfield variant (something to hang onto ahead of you), a split stance allows even individuals with long torsos to keep weight atop the spine without the typical need for excessive forward bow.
Unilateral exercises help uncover weakness in specific structures, low activation in one side, or just incite the focus to draw more intensity out of whichever side is currently working. Within this discovery is usually a fairly important subset of findings about foot placement and how most people place feet during bilateral exercises in positions which could never even approximate optimal performance once they take one off the ground.
Balance, strictly speaking, is largely borne out of strength (ie - force production capacity and speed). Working one side allows us to encounter more precisely the foot placement and stress distribution which will occur when directing strength and balance in the real world. In short, you'll have to balance on one side at some point. Why not practice?
The hip, the glute max, med, and surrounding tissue is generally weak in the average person, even in some high level athletes I've encountered. No matter what, though, with both feet planted, they can push against one another in a transverse lever. That is, they can direct pressure away from each other in order to create central tension that moves us upward in the frontal plane. Split stance reduces this without eliminating it entirely like one would with strict single leg exercises.
It's easier to be clear about range of motion sans visual feedback. You can, indeed, use tactile feedback for a standard squat or even a box squat. Split stance has more obvious upper and lower limits of range. A step underneath the front foot can increase ROM. A bolster underneath the front knee can reduce ROM. But shifting the body forward or backward has little to no fudging impact on this, unlike with box squat where one can throw the hips backward far enough to touch the box with hamstrings at a shallower depth than even the prior repetition. Even in deadlift, a bar which bends begins to obscure the return travel distance from the second rep and after.
IG post and video here: https://www.instagram.com/p/BwCU-cpjRwX/