AFAIK the main reason is weight. The standard vests are a fabric, like a shirt (sorry for the over simplification). As mentioned in the other response these fabrics slow a bullet down to zero. It can still break your ribs, so. On the other hand, a knife cuts through these fabrics as it will cut through a shirt. A solution is to put "plates" in the vests at critical points, they also offer additional ballistic protection.

Downside is these plates aren't flexible (conformt is an issue if have to wear your vest all day at 30° C in summer) and they become heavier and more bulky.

But again, that's what if been told by some german cops and I'm no expert in that.