I sure agree about the sum of squares, but I think Gauss main motivation before that was his assumption that the error curve has to be differntiable, i.e. squared vs absolute error

> Gauss derived ‘his’ curve by extending these two properties with: (iii) the error distribution should be differentiable (thus,

excluding Simpson’s and Laplace’s suggestions)

https://pure.rug.nl/ws/portalfiles/portal/64850760/59637459_4037058_naw5_2018_19_1_037.pdf