Eren surmised that Greater Skills were similar to Authorities.
Unlike the Skills that could be gained easily through Menaka's Blessings, the acquisition of Greater Skills wasn't so simple. It had special requirements.
Plus, not everyone could wield them. They were reserved for special entities. And most of these special entities had direct connections to the gods or Demon Princes.
Menaka was a neutral goddess. So she facilitated the gods and mighty demons to maintain close ties with some of their followers. The Menaka's Blessing was a way for the followers to obtain Perks and other blessings from the gods they idolized.
As for the Edicts? Eren wasn't sure if he could use Edicts through the use of Menaka's Mesh. After all, Edicts could only be wielded by divine beings.