I cannot speak for eanzenberg but I think his comment was less about his personal justification and more about the rationalizations that have been used in the history of stats.

Gauss quite openly admitted that the choice was borne out of convenience. The justification using Normal or Gaussian distribution came later and the Gauss Markov result on conditional distribution came even later.

Even at that time when Gauss proposed the loss, it was noted by many of Gauss' peers and (perhaps by Gauss himself) that other loss functions seem more appropriate if one goes by empirical performance, in particular the L1 distance.

Now that we have the compute power to deal with L1 it has come back with a vengeance and people have been researching its properties with renewed almost earnest. In fact there is a veritable revolution that's going on right now in the ML and stats world around it.

Just as optimizing the squared loss gives you conditional expectation, minimizing the L1 error gives you conditional median. The latter is to be preferred when the distribution has a fat tail, or is corrupted by outliers. This knowledge is no where close to being new. Gauss's peers knew this.

I think just historically it's interesting. Every statistician was using OLS before computers because they could solve it with pen and paper, so when computers came out it was ported over. But with computers you can minimize any loss function.

However it is useful to have a closed form solution because it guarantees you actually minimized it. Other strategies to minimize functions don't guarantee that but they're still extremely useful.