It works if you use MockMvcTester.perform(RequestBuilder) and RestDocumentationRequestBuilders but this loses much of the benefit of MockMvcTester as you then can't use its fluent API to build the request.
spring-projects/spring-framework#33509 will make the URI template, if any, available from MockHttpServletRequest. REST Docs should use it with Framework 6.2. This will allow the fluent MockMvcTester API to be used to build the request and also remove the need for RestDocumentationRequestBuilders when using Framework 6.2.