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Coming from a structure of . . .
. . . instead of 1-level and 2-levels down, I only get:
. . . by going to Settings > Permalinks and setting up Custom Structure like . . .
- /%category%/%postname%/
. . . but why can't I use more levels in organizing blogs?

You can. Go to Posts > Categories and set your “dir2” category to be a child of the “dir1”. WP will automatically use your desired url structure.
More info https://www.wpbeginner.com/wp-tutorials/how-to-include-category-and-subcategory-in-wordpress-urls/