Two parter:
1. Can Wildling also be used for wounds and attacks like the other class characteristic increases?
2. Should the Greater (Level 2) Class also have access to wildling? It seems to be present in all other class levels, wondered if it was an oversight.
1. Yes they can use Wounds and attacks for Wildling.
2. No for the Level 2's on having it. It was intentional. Level 1 and 2s in Biests are rather similar when first building them, with level 2's having greater room to grow. Essentially better natural weapons, (due to a higher maximum properties and more possible class traits).
Level 3 Classes for the Biests really stand out on the tabletop. One of the stronger Level 3s of the domains (although the point costs will equate that).
There was a debate on Level 3's and 5's having it as they had a greater upgrade version of Wildling during playtesting. It was overpowered and toned down to just wildling. We were fine tuning gameplay, so I do see your point though on the overall Consistency looking at the classes.
I think you will find that the Biests are quite literally the Masters in straight stats.