This combination – localized Dijkstra, super-fast abstract graph traversal, and highly localized A* refinement – is what delivers the 100x speedup.
Point lookups are useful, but the operation you'll reach for more often is a range query: give the tree a rectangular region and retrieve every point inside it, without scanning the entire dataset.
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The pruned nodes (in red) represent entire regions of space that the algorithm never examines. The points inside those regions are never checked. Compare the "Nodes Visited" count to the total number of points. The quadtree is doing far less work than a brute-force scan.