Flat points take advantage of a concept called Supercavitation. A high-velocity projectile with a flat point will create a high center of pressure at the nose of the bullet. At a certain pressure threshold*, this pressure forces the fluid radially outward at a velocity high enough that the "hole" left in the fluid ahead of the projectile is larger in diameter than the projectile itself (the "super" meaning "ahead of").
The advantages are two-fold:
1) First, that the fluid is actually not contacting the sides of the bullet means reduced friction, which means greater and straighter penetration.
2) That larger-than-caliber "hole" punched through the medium can result in permanent wound channels significantly larger than the bullet diameter. The results are harder to find because the mainstream is all focused on the latest fancy JHPs, but if you dig around you will find many results of 1.5"+ wound cavities with depths of 24-48 inches using bullets having meplats of, say, .35" to .40" pushed to velocities in the 1200-1400fps range.
Conversely, the tapered edges of the expanded mushroom of a typical JHP do not induce the same radial velocity in the fluid as the nominally-flat central area. Thus, they tend to generate more friction for a given tissue displacement, which is why they stop much earlier than a WFN despite similar overall wound diameters.
In the .45 Super thread, es350 reported the following results:
A 215gr WFN bullet with a .38" meplat, pushed something around 1350-1400fps, made a permanent wound about 1.5-1.75+ in diameter all the way through the animal.
A ~200gr XTP (not 100% sure of the weight of the top of my head) pushed at a similar velocity made a 1.75-2" permanent wound cavity in the first 6" of penetration but which tapered down closer to caliber-sized after that.
Google "wide meplat permanent wound cavity" and you will find los of threads, with pictures, showing similar results.
*edit: forgot to add*
*That "certain velocity" is a function of bullet diameter, meplat diameter, and fluid density / cohesion. Most any bullet fired into water will make a big splash as large volumes of fluid are displaced by that center of pressure. Tissue, obviously, is much less fragile, but the end effect of having tissue displaced to a diameter greater than the bullet--even to such a large degree that a volume of tissue well beyond bullet diameter is damaged beyond function--is very real and very common.
Long story short:
JHPs came about as an improvement over round-nose bullets, and they are. They were justified to the public by over-hyping what is barely more than the myth of "over-penetration resulting in hitting innocent bystanders," but the underlying goal was to get more effective ammo for police officers. The reason WFN bullets are not more widely used is a combination of feed reliability (in both autos and revolvers) and the continued belief that there is a small child cowering behind every would-be murderer.
I often run FWCs in my G21, and would absolutely keep the first cylinder stocked with them in a revolver.