If you think your art director should be hands-on and produce directly usable in-game content or illustrations, either your team is very small, or you have grossly underestimated the task on both ends.
Being an art director requires one to look at the big picture, adapt ideas and provide solutions depending on constraints (tech, visual, design, time, etc). The AD will usually work with their art team but also, and very importantly, with other departments to research & develop those.
Finally, an art director’s primary role is that of providing leadership, vision and communication. Their responsibility is to synthesize the global vision & identity for a game, and communicate it to the team, so they can
1. Buy into it
2. Understand it
3. Support it
4. Enrich it
Asking an AD to work on producing art of any kind requires them to devote a lot of focus, time, and an attention to detail. If an AD is busy doing that, then they are not available for the devteam or their artists. That’s a pretty bad situation.