The role of the root switch after Spanning Tree Protocol has established a tree network in a LAN?
I can find no requirement that all traffic is routed through the root switch. For example, in A&lt;-->B&lt;-->C, with C the root switch, traffic fom A to B does not pass through the root switch.

The spanning tree protocol first selects a root switch. In Cisco, this is the switch with the lowest bridge ID. So the selection of the root is arbitrary. Now a tree is built that connects all switches, without creating cycles. Even if initially a minimum spanning tree is created because links with maximum bandwidth (minimum cost) are selected, at some future point this may no longer be when a link fails and a redundant link or path is enabled. This new link may result in the total tree not being a minimum spanning tree anymore. I can imagine that reconfiguring the whole tree to be minimum again can cause unwanted overhead.

I found this information on Wikipedia and Cisco. I am not a network guru so my answer may not be complete. I found no information that the initial tree created is minimum though it seems to meet the requirements and seems to follow e.g. Kruksal's algorithm.