The generalized PL Poincare hypothesis states that in dimension $n$ there is a unique PL manifold that has the homotopy-type of $S^n$. It's known to be true in all dimensions except perhaps $n=4$.

For $n \geq 5$ the standard argument uses rather explicit handle manipulations to come up with the proof (proving the h-cobordism theorem in the process), which is somewhat spiritually-similar to (although more complicated than) the proofs in dimension $n=2$.

The proof in dimension $n=3$ is very different than the above two cases.

But I wonder, perhaps there is a proof that avoids the h-cobordism theorem, perhaps there is a more direct proof? Has there been much discussion of this in the literature?

One thought would be to find an appropriately simplified proof of the Farrell fibering theorem (when a manifold fibers over $S^1$), one that perhaps allows you to reduce $S^n$ recognition into a homotopy-unknot recognition problem.

I imagine back in the 60's and 70's there was some discussion of these topics but I wouldn't know where to look.