On chess specifically, my takeaway is that the branching factor in chess never gets so high that a breadth-first approach is unworkable. The median branching factor (i.e. the number of legal moves) maxes out at around 40 but generally stays near 30. The most moves I have ever found in any position from a real game was 147, but at that point almost every move is checkmate anyways.
Creating superhuman go engines was a challenge for a long time because the branching factor is so much larger than chess.
Since MCTS is less thorough, it makes sense that a full search could find a weakness and exploit it. To me, the question is whether we can apply breadth-first approaches to larger games and situations, and I think the answer is clearly no. Unlike chess, the branching factor of real-world situations is orders of magnitude larger.
But also unlike chess, which is highly chaotic (small decisions matter a lot for future state), most small decisions don't matter. If you're flying from NYC to LA, it matters a lot if you drive or fly or walk. It mostly doesn't matter if you walk out the door starting with your left foot or your right. It mostly doesn't matter if you blink now or in two seconds.