elastic search copy_to field not filled

I believe that you can achieve what you want without copy_to. Let me show you how and why you don't need it here.

How can I make both full-text and exact match queries on the same field?

This can be done with fields mapping attribute. Basically, with the following piece of mapping:

PUT producten_prd_5_test_new
{
  "aliases": {},
  "mappings": {
    "boek": {
      "properties": {
        "hoofdtitel": {
          "type": "text", <== analysing for full text search
          "fields": {
            "keyword": {
              "type": "keyword" <== analysing for exact match
            },
            "suggest": {  
              "type": "completion",  <== analysing for suggest
              "analyzer": "simple",
              "preserve_separators": false,
              "preserve_position_increments": true,
              "max_input_length": 50
            }
          }
        }
      }
    }
  }
}

you will be telling Elasticsearch to index the same field three times: one for full-text search, one for exact match and one for suggest.

The exact search will be possible to do via a term query like this:

GET producten_prd_5_test_new/_search
{
  "query": {
    "term": {
      "hoofdtitel.keyword": "The Nature of the Firm in the Oil Industry"
    }
  }
}

Why the field exact_hoofdtitel does not appear in the returned document?

Because copy_to does not change the source:

The original _source field will not be modified to show the copied values.

It works like _all field, allowing you to concat values of multiple fields in one imaginary field and analyse it in a special way.

Does it make sense to do a copy_to to an index: false field?

With index: false the field will not be analyzed and will not be searchable (like in your example, the field exact_hoofdtitel.keyword).

It may still make sense to do so if you want to do keyword aggregations on that field:

GET producten_prd_5_test/_search
{
  "aggs": {
    "by copy to": {
      "terms": {
        "field": "exact_hoofdtitel.keyword"
      }
    }
  }
}

This will return something like:

{
  "aggregations": {
    "by copy to": {
      "doc_count_error_upper_bound": 0,
      "sum_other_doc_count": 0,
      "buckets": [
        {
          "key": "The Nature of the Firm in the Oil Industry",
          "doc_count": 1
        }
      ]
    }
  }
}