While on the map, when the unit is moving around, it's hard to show promotions more distinctly than a simple number. When you've highlighted the unit, the promotions are visible easily. The computer's graphics requirements for Civ6 (and future Civ7) will be powerful enough to render a small 2x3 box with colored/darker boxes for promotions earned. Probably could do that for consoles also.
But I can understand your use case: if I have two or more units who could attack, which unit do I want to attack first, next, and so on? Being able to see something about their promotions *before* I select them would save me some clicks. Even something simple like chevrons > >> >>> could help, without taking up too many pixels. IIRC, Civ3 used stacked dashes for conscript/regular/veteran/elite.