This problem was caused by the initial decision of limiting each search index to a single entity (or other) type – since normal searches are always executed on a single index, a search across multiple types cannot be created this way. While other, maybe better-working workarounds in Drupal 7 would be possible, this is solved completely in Drupal 8 where this restriction doesn’t exist anymore. You can now use any number of item types (or “data sources”, as we now call them) for a search index, and even change them completely at any time later on, which makes searches across entity types, or even over both Drupal-internal and external data, work exactly as smoothly as searches on a single entity type did before. This makes it possible even for a large site, with lots of different types of content and associated searches, to use a single search index for the whole site. When creating a search (view), you can then just filter by the appropriate types to get a type-specific search.