Very likely Jarque and Bera following the Pearson´s test on normality and thought that were most smart in adding the Skewness and Kurtosis estimators after normalizing (Kurtosis excess) and squaring them using the variances 6/n and 24/n. Once getting the squares of two normal r.v, each one follows a one-degree of freedom chi-squared law, the sum a two-degrees. . . . Et voilà!___ (and so there)! .
Remember that Pearson even then defined: ___b1= m3/(m2^3/2)___b2= m4/(m2^2) But the decision was depending the critical values(cv), ___Reject if |b1|> cv1(1-alpha/2), or _____ if b2 outside [cv2(alpha/2, cv2(1-alpha/2]
J-B did not refrain to go further___and crash . . .