Yes paintings are useful. Paintings are no more or less biased than any other media inherently. People who record history, tell their own stories and often those stories are biased. It's the historians job to Judge the value of the depiction of events and historians use all the sources they have, even biased sources to come up with as complete a picture as they can.
- Bayeux Tapestry(tapestry).
- The Roman battle of Battle of Philippi. (tapestry).
- George Washington's image crossing the Delaware(painting)
- The Battle of San Romano 1438–40(painting)
- The Surrender of Breda, 1634-1635(painting)
- The Death of Major Peirson, 1783 (painting)
- Raising of the American flag over the battle of Iwo Jima. (Photograph)
A painting can be as useful or not useful as a photograph, a tapestry or even a written record; depending upon the knowledge, motivation and intent of the source.
A painting is just another media used to tell the story, it has to be evaluated, studied and understood like any other piece of the puzzle in understanding the complete picture.
As for this particular painting. It shows the battle being a mele. My sources refute that. My sources report the British were organized and showed well against a numerically superior (German had a 2-1 advantage in troops) enemy initially. This painting represents the aftermath of the battle.
The battle was early in WWI, the British BEF fought well, but were significantly outnumbered. They ultimately were forced to withdraw when supporting troops guarding their flanks withdrew. British withdrawal started out orderly. The withdrawal however took two weeks and had the British retreating almost to the outskirts of Paris before counter attacking. So this picture represents what happened after the battle, when the retreat became disorganized. Only part of story. Maybe the most important part of the story for the British troops at the Battle of Mons.