Hey Chaim Yankle,
I think your question is a valid question even for people not struggling with shmiras Einayim. To be honest, i don't have, or hve i ever participated in social media platforms (bar LinkedIn) so i might not be the best person to comment, but i'm going to anyways:
My understanding is, like you said, there is a lot of shmutz and wasteful stuff which is useless, and just wastes precious time and brain space. I dont know what "fun and education" you refer to, but am i mistaken that you can't do that on whatsapp group, or get education on the internet...
I definitely think that it is worth coming to some sort of compromise with your wife on this issue, both in terms of general and Shalom bayis.
I'm happy to discuss further if you so desire, either by email/hangout or via chat-
360gye@gmail.com