A bivy, waterproof or not, cuts a lot of wind and can make all the difference if you are in an exposed location. Same for bugs. I have used one to help keep my expensive down bag clean.

A completely non breathable Bivy can work best for short term use in stopping the evaporative heat loss of someone who is wet thru and in cold or windy conditions. Say a few hours while waiting for dry clothes or evacuation to arrive. A large trash bag will do the same. Allowing evaporation thru a breathable Bivy would make the person colder.

A breathable Bivy can allow moisture to escape and in the right conditions can allow your sleeping bag and or clothes to dry over time. As long as one has enough insulation or heat, this would be a good long term method.

If your breathable Bivy is wet all over the outside, water vapor from inside can't escape. The use of a tarp as mentioned, or even tree cover, can help.

In heavy dew conditions, the dew point can be inside the Bivy (or sleeping bag shell for that matter) and the Bivy will appear to not be doing it job. Extra heat in side the sleeping bag or Bivy will help drive the moisture (move the dew point) toward the outside.

I like a Bivy with noseeum netting, a breathable top (not Goretex, which is heavy) and a coated nylon floor. The one I use is about 8 oz. Light enough to take most anytime I go out. I combine it with a little 5x8' tarp that also weighs little and with 40 ft of cord have a 1 lb package good for wind, rain, snow and bugs.

Dressing or cooking from a Bivy alone is more difficult in heavy weather, the tarp helps that.