I believe you meant, "uninterpreted", and your comment is refuted by 1 Cor 14:4 "One who speaks in a tongue edifies himself". Yes, edification of the church is greater; that is not contested.
Pagan worship practices are irrelevant. Paul is not referencing them in these chapters. The word "mysteries" simply means "things unknown to men". There is no esoteric meaning to it in this context.
12:7 gives a general purpose for the gifts. It doesn't preclude edification of the individual within the body. When one person receives healing, do all receive healing? Paul is explaining how to use the manifestation properly
in the church. If Paul were simply condemning its abuse, he would not likely have summarized the passage by saying, "and do not forbid speaking in tongues."
Since you seem to believe that "edifies" is a bad thing, find the word (or any variant) in Scripture that is
clearly negative, not counting this one which
you claim to be negative.
Paul states that when a person speaks in tongues, he edifies himself. The context suggests that without interpretation, the church is not edified, but it doesn't even hint that it is in any way injured. Further, the context makes it clear that the church
is edified when the tongues-message is interpreted. Nothing further is stated regarding the whole group; to answer your question further, I would have to resort to arguing from silence.
If someone (whom you appreciate!) gives you a hug when you're feeling down, do you feel better? Are you 'edified'? Do you understand it? Does your mind rationally process everything that happens in your body and your inner being when you receive a hug? Paul says that speaking in tongues edifies the speaker, and edification is a good thing. I don't need to understand everything rationally to accept the validity of it.
As to your last sentence, "Yet this is not allowed correct?" Is it allowed incorrect? Yes, I'm being a grammar Nazi.