Why is it conventional to set line width > nozzle diameter? I recently became curious about the Line Width setting in Cura and why one might change it if they aren't using different size nozzle.

Since I've gotten my Ender 3, I've always kept the line width equal to my nozzle size (0.4 mm). I've looked around a bit, and it seems like most people actually set their line widths to be higher, depending upon who you ask anywhere from 120 - 150 % nozzle diameter. 

Why is this? They mention that it helps with print adhesion, but why? Shouldn't a 0.4 mm nozzle create a line of plastic 0.4 mm wide, necessitating a line spacing of 0.4 mm?
There are several things at play that can make a wider line nice to have:
First layer adhesion
Due to some filaments having serious struggle to get the first line or layer stuck to the bed, it can be an easy fix to just increase the line width, generating a bigger Adhesive Force $F_a\propto A(l,w)$, where A is the area covered by the line, and thus simply $A=l*w$ with length l and width w of the line. So, a wider line means better initial adhesion and can lead to less failed prints in layer 1.
Plastic Goo
Plastics under heat behave in certain ways: they turn into a gooey substance that expands. This is also the reason why prints shrink a little as they cool. Now, if we press the plastic onto the bed with more force (as we force more plastic through than before to go from 0.4 mm to 0.5 mm) for the first time, we have a roughly flat area. The extra filament will make a wider line. The slicher can account for that, and does.
Now, next layer up: Where does the extra material go now? Plastic goo has one property that is very interesting: it tries to shrink its surface as much as possible. Heat a short piece with an airgun and it gets a little beady. But on the other hand, it comes hot enough from the nozzle to melt a tiny surface area of the already built layers, which is how layer bonding works in the first place. But our goopy plastic finds the layer below not exactly flat like the first layer found its lower surface, it finds a shape of ridges and valley. Taking into account that it wants to have the least surface to non-plastic (=air) and slightly cross bonds with the print, it will fill these nooks and crevices inside the print a tiny little better, as the increased force we use to push it out also increased the speed at which it expands to them: we reduce the time a tiny bit to reach there. How does it matter?

Well, heat transfer bases, roughly speaking, on a formula like this: $Q = mc\Delta T$ Q is the thermal energy of the object, m the mass of the object, c its specific heat capacity and T the temperature, ΔT the temperature change. But we don't have a homogenous object, we got pretty much a heat distribution with touching zones of different heat. The actual formula for the heat transfer inside the object is a long mess containing stuff like the gradient $\text{grad}T$, thermal conductivities, and integrals, but what matters is the result: The faster-expanding line of filament loses a little less thermal energy to its surroundings than the less forceful extruded line, which can increase the bonding between the two as the temperature on several fronts:

it enters the crevices further before reverting from goo to solid, leading to better adhesion for more surface.
it contains more thermal energy that can and will get transmitted to the layer below and has a bigger surface area, so it can increase the zone thickness that gets remelted a tiny bit, increasing the layer bonding strength a little.

This can result in a problem though: if you don't give the printed lines enough time to cool, it can lead to the material to accumulate heat more and more, leading to the whole thing to melt and turn into goop. An easy fix to this side problem is minimum layer time. But that would be only tangential to the original question, so look for example at the question here or the video the thermal picture above is taken from here.