There’s a masochistic streak to the British psyche that enjoys a defeat if it can be dressed up in a good story. See Dunkirk. Goes hand-in-hand with a liking for the underdog tale (real or imagined), hence the love of battles like Agincourt and Rourk’s Drift (both of which were strategically fairly insignificant).
The light brigade I find extra strange because it totally eclipses the whole battle it was a part of. Most armchair MilHist Britons could tell you next to nothing about Balaclava beyond that charge. They’d literally rather remember that embarrassing failure than the victories because it’s got that whole heroic tragedy vibe. The heavy brigade and the highlanders would definitely like a word.
If the Charge of Light Brigade had happened in the US Civil War, it would had barely made it to the dispatches.