In a general, asymptotic, worst-case setting, there are no algorithms that are known to find a shortest (s, t) path any faster than computing the entire shortest-path tree.
Nonetheless, there are obvious inefficiencies in this approach.
Consider route finding in 2d in which t is on one side of s, and all other nodes are closer and in the other direction. Dijkstra's ``looks where the light is good'' in some sense.
Note: This is not a typical ``algorithms'' topic, but it's pretty cool, pretty useful, and an AI thing.
