I would say the need for a bivy in a tarp shelter really depends on too many variables to narrow it down to a generic explanation. Temperature, humidity, wind, how well you seal up the bottom, if you vent the top, etc.
I recently had three of us sleeping in my 2 man Mountainsmith tarp for close to a week. Temps were about 35-40 during the day and about 15-25 at night. We got hammered with nonstop squalls for a day. It was very windy and we piled deadfall/snow up the perimeter to seal the bottom to the ground and closed the vents to keep spindrifts out. Two of the three bags (all down) were goretex with worn out DWR. One bag (that we placed in the center to protect it) had no protection for the feathers and was only a 20 lower EN rating, so he used a sol "breathable" bivy. I use a sheet of 2 mil LDPE painters plastic under my pad. The condensation was freezing to the inside of the tarp quickly due to the cold, so we did not have much drippage, but everyone was brushing the tarp all night due to the cramped conditions, and we had frost all over our bags all night. The day after the squalls subsided, I made clotheslines and hung ALL our gear up immediately. The goretex bags were damp on the surface due to the DWR being worn out, but obviously the teflon underneath protected the feathers just fine from frost (liquid water may have made it through the baffle stitching at a very slow rate). The non-protected bag's exterior that was inside a bivy was saturated inside from breath/perspiration over the last three days. The untreated nylon exterior had wetted out, but the feathers were not clumpy at all. I hung the bags in the breeze and turned them inside out after a bit, and the non-protected bag was totally dry in a half hour. The goretex bags probably didn't need to be hung, just brushed off and left in the tarp with the door open.
In the summer when I use a different bag or a quilt that is not water resistant, I usually lay a sheet of plastic over part of my insulation if it is conditions where I will experience significant condensation inside the shelter (it has to do with temp/wet bulb/dew point). I prefer a sheet of plastic that still gets airflow to a bivy because a bivy can trap moisture. On the other hand, plastic can get blown away/slide off. It really depends on how you sleep, your shelter's shape, your weather, etc. The big thing is you need to understand the advantages and limitations of your equipment and plan how you'll use it effectively in the weather your will experience. If you're in a tiny sheep tarp in a chinook, a bivy is probably going to be more practical, but you need to pack your bag away in a waterproof sack and wipe out the inside of your bivy every morning. If you're using a sheet of plastic, you need to pile rocks around the perimeter to keep the wind from blowing it off the bag and letting it get wet. If you're in a big tarp with a lot of protection, you're probably best off to use a non-goretex bag that breaths better and use the large interior air space to your advantage and vent the shelter strategically to keep the inside humidity to a minimum.