It's definitely something we are aware of and plan to address at some point, but we have no concrete plans for this feature at the time.
If you simply need to store data for lookup later, and don't necessarily need it for filtering, you can upload it as a serialized JSON string that you can then unserialize when rendering the result.
EDIT: I originally said "and don't necessarily need it for search or filtering", but then I changed it to just filtering. The serialized JSON would actually be searchable. However, it wouldn't be valuable to show the user a serialized JSON blob so you'd need to deserialize it when rendering in the search results.
And one more thing to point out, if you send a nested object currently, it will automatically be converted to a string by App Search, so there's no need to do the serialization when indexing.
Hope that helps,