All of my personal bows are asymmetrical. I prefer how they balance in the hand to carry, and how they balance during the draw.
It's actually easier to dynamiclally balance their limb strengths during the draw than it is to balance a symmetrical bow because the asymmetrical bow's critical factors regarding dynamic balance are generally more closely aligned to begin with... bow center/static balance point, and the fulcrums under our hands. Their closer proximity to one another means less movement of the dynamic/sliding fulcrum under the bow hand as the draw transpires... which makes it easier to navigate during tillering(if tillering for dynamic balance) and feels better in the finished bow.
If I was making a bow for someone who was string walking or had a low fixed crawl I'd reassess bow center location and maybe then a symmetrical design would get those things better aligned, for them. Depends.