My driving licence is my personal property and contains personal information that they are not entitled to have so I would not hand it over. If ID was needed that should be provided by my employer.
When I worked on freight out of Heathrow many years ago I had security ID to go airside, even that did not require me to had over any personal documents.
BTW: What’s a reducer? I had always thought it was a plumbing component to reduce pipe sizes and nothing to do with trucks.