I totally agree with the Op. It doesn’t make sense to use cover directly… because character model just don’t use advantage of it (yet/it’s a bug?). Sometimes it does seem to use it like cover but 99% of time it’s only an obstacle of certain height in the line of sight.
For me it would be perfect if we could have crouch action (like 25% AP, maybe reduced to 0 with a skill, like with reloading). Character would “hug” the full cover and lean left or right while shooting, similar to Firaxis X-Com (that’s the aspect they did very well). And the half-cover would need the crouch action to be used (and AP spent) to use it as a cover. Without crouching it would behave exactly like it is right now, an obstacle that covers only part on model.
Crouching would also be usefull in open space, to reduce sligtly the visual signature of your model.
This is also an issue of highground advantage not used at all: BB5 Windows and top floor cover
Sniper on a crane (where the blue “strategic spot” area is), on a scrapyard-like map, can’t shot anything because floor is an obstacle and he refuses to lean out even a bit. Or maybe make lean left, right, forward manual with a keyboard while aiming? It could trigger Overwatch to not make it without flaws.