The most common and most likely answer to this crossword clue is the 1 plus 5 plus 4 letter word A MUG’S GAME
I've seen this crossword clue in Financial Times
A
M
U
G
â
€
™
S
G
A
M
E
Buddy explains!
The straight part
We know that "Something only a fool would do" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case something only a fool would do = a mug’s game.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.