An implementation of ServletContainerInitializer can't add a mapping to "/" because the default servlet is loaded first, as first reported in 51278:

public final class SampleServletContainerInitializer implements ServletContainerInitializer {

  public void onStartup(final Set<Class<?>> c, final ServletContext ctx) throws ServletException {
    final XmlWebApplicationContext appCtx = new XmlWebApplicationContext();

    appCtx.setConfigLocation("/WEB-INF/DispatcherServlet-servlet.xml");

    final ServletRegistration.Dynamic dispatcher = ctx.addServlet("DispatcherServlet", new DispatcherServlet(appCtx));

    dispatcher.setLoadOnStartup(1);

    final Set<String> conflictSet = dispatcher.addMapping("/");

    for (final String conflict : conflictSet)
      out.println(conflict); // prints "/"

  }

}

A test case follows attached.