So, this is the problem as i see it: once the oiled-cotton filter gets dirty enough that all the oil dries out, it’s possible for dusty air to make its way through the more porous filter media and into your engine, whereas a paper filter with it's much smaller voids would simply become blocked.
Am I missing something?
You are certainly asking the correct and smart questions.
It helps to consider a couple of differences. How are cotton and paper made? The cotton media is woven, the paper media is soaked and pressed flat. Then consider the difference between air and dirt. Air molecules are obviously much smaller and, in turn, much more "fluid"(fluidity). The air can weave its way through either material better than can dirt.
Next consider the construction. When you grab a woven cotton filter, like K&N, you will notice the stainless steel screen on both the inside and outside of the cotton. That allows the material to be thicker and hold the pleats which are also deeper, providing more surface area (that also adds to the expense). Picture the dirty air having to race through a slalom course. The air molecules win. Then it is a mater of scale. The distinction is fluidity not porosity.
Staying on the subject of construction for a moment longer, notice the difference between soft wider rubber gaskets compared to hard narrow plastic. Then picture micro-pounding(bouncing) from vibration those gaskets experience while trying to maintain the "coastline" seal against dirt particles.
Back to one part of your specific question,
"...whereas a paper filter with it's much smaller voids would simply become blocked." Actually that would be nice buy way, way before a paper filter gets literally blocked the suction of the intake will simply pull the dirt particles through the material. You might notice a bit of slower starting but it will still run.
In the end both types have a finite duty cycle. The dirty air we ride through is the same for both.