I would motivate the simple loop conjecture as follows. (I'm fairly idiosyncratic about this; I fear I'm going to turn off many 3-manifold topologists.)
As well as understanding spaces, we want to understand the maps between them. One instance of this is that it would be extremely useful to have some sort of 'classification' of the set of all maps from your favourite (closed, say) surface $\Sigma$ to any 3-manifolds
What might such an understanding look like? If we replace 3-manifolds by graphs, then the answer is provided by a folklore theorem, often attributed to either Stallings or Zieschang.
Folklore theorem: Every continuous map from $\Sigma$ to a graph $\Gamma$ kills an essential simple closed curve.
This fits into Sela's framework of Makanin--Razborov diagrams (over free groups), where it implies that the natural homomorphism $\pi_1\Sigma\to F$ induced by including $\Sigma$ in the boundary of a handlebody forms the Makanin--Razborov diagram for $\pi_1\Sigma$.
So the simple loop conjecture is the analogous statement over 3-manifolds. Basically, it would take us from having a relatively hazy understanding of what the set of all maps from $\Sigma$ to a 3-manifold might look like, to a fairly complete understanding.
You might say "Fine, but what's so special about surfaces?" In fact, surfaces play a distinguished role, because of the way they arise naturally in JSJ theory. For this reason, they are one of the key cases; if we can understand maps from surfaces to 3-manifolds, we have a chance of understanding maps from arbitrary aspherical spaces to 3-manifolds.
Best Answer
Property R was reproved by Gordon and Luecke in the course of solving the knot complement problem - see Corollary 3.2. They prove the stronger result (as did Gabai) that zero-frame surgery on a knot is irreducible (hence cannot be $S^1\times S^2$).
Gabai actually proved something slightly stronger, which might account for the increased difficulty of the proof, namely that there is a taut finite-depth foliation which intersects the boundary of the knot complement transversely in a foliation of the boundary torus by longitudes. Capping off this foliation with a foliation by disks in the solid torus gives a taut foliation of the zero-framed surgery, hence irreducibility.
Gordon and Luecke use many of the techniques of Gabai (thin position, Scharlemann cycles and generalizations), but omit the foliations and sutured manifold hierarchies. A technical simplification to the argument was subsequently made by Walter Parry.