How to assign keyboard shortcut to Picker

Adding a picker to commands works very well, but how can this be made to work with keyboard shortcuts? Adding .keyboardShortcut does not appear to have any effect, even if wrapped into a Button.

struct EditorCommands: Commands {
  @State var selectedTool: Tool

  var body: some Commands {
    CommandGroup(after: .pasteboard) {
      Divider()
      Picker("Select tool", selection: $selectedTool) {
        ForEach(Tool.allCases, id: \.self) { tool in
            tool.labeledToolbarImage
              .keyboardShortcut(tool.shortcut)
        }
      }
      .pickerStyle(.inline)
      .labelsHidden()
    }
  }
}