Really wonder who in his right mind, who can also read a book, would decide to do so in order to enumerate the sequences of items…

Vectors are traditionally written as columns, so just writing all the columns in left-to-right order into a bigger column makes sense. The confusing bit isn't the ordering of the elements in a matrix, it's that someone decided to write vectors as columns to begin with!

The plus side is that you can use row vectors with matrices acting from the right, and keep the traditional matrix multiplication. Rare case of two wrongs creating a right.

It took me long while to stop being afraid when people wrote vec^T where ^T means transposed. I was like "but why can we do that", and the mathematician answered - "well, because it is just more convenient this time". o_O