Or is it just our believe that end users will fill this field and the missing awareness on the interdependency with performance?
Not a problem at all. Running V.00 (or any of the transactions similar to this one) is part of the list of daily/weekly/monthly tasks assigned to different teams, so the users are aware that they should process these documents.
As to your client, I do not really know what are their processes, the number of incomplete documents within a specific period and the impact of not completing them in a certain time-frame, so it is hard to advise which team and how often should review and process documents generally incomplete.
In all cases, it would be a good idea to check whether incomplete document processing was part of the regular tasks of any specific team, with what selections, etc.
If it was not part of anybody's responsibilities, then the business needs to decide which would be the most appropriate role for each specific case.
If this processing was expected to be performed regularly, but it did not happen, I would wonder what other activities they could have skipped. It seems worth investigating further.