In the scheme from the article, each new outer ring starts from the same position (bottom left corner of the hexagon), which seems a useful invariant
This also causes you to lose equal distance steps for each increment because you have to "jump over" to get to the next ring. That seems like a useful invariant for a coordinate system too.
This was my first instinct as well, which makes sure numbers are adjacent. OP also mentioned this variant as lucidBrot/hexgridspiral in the older post.
Good question. That seems a lot more symmetric and easier to use.