A* is not limited to point-to-point, it also handles point-to-set-of-points just fine (you just might have to reverse the direction you're thinking in). Although this is most often used for "we only need a path to one of them", it's still faster even if you need a path to all of them due to merging. Visiting all points (as BFS does) on the graph is rarely what you actually want (though admittedly, if you're able to throw away the grid it becomes more likely; like the article, I do find people use grids far too often).
BFS works just fine with variable edge weights, you just have to use a priority queue instead of a plain queue for the next set of nodes to be visited.
