Family and small communities are very much valued by Green, yeah.
This enchantment comes to mind, (look at that art! Best green art in the game imo). There's definitely 'rules of nature' aspects to green, about being a little selfish and allowing the strong to prey on the weak (especially if we pick up black secondary. It's the strongest overlap there really.) But there's also a lot about community and growth, and helping people get along I think might edge into green because of it's adjacency to white.
I think a green overchannel might cause us to try and grow past our parents, really. A lot of green effects are about pushing you up several rungs in the natural order, effectively (sometimes literally, sometimes just giving you a lot of
authority) and that would work to help a lot of our problems. It could also make us really chill and accepting our place in the universe and communing with nature-y, but I think overchanneling usually involves gaining strength, whatever color it is, rather than just aligning your mindset to that colors philosophy.