The Turkish Cypriots will not agree to any plan that does not contain guarantee rights of Turkey. This is one of their red lines. I also would prefer, just like anyone else, to have a country that is not dependent on guarantee rights of the motherlands but I cannot see this happening and this is a compromise I am willing to accept in order to reach a solution.
The Cyprus issue belongs to the UN and the EU has no jurisdiction over it. Sometimes we behave as though we are the only people that matter and when we say Cyprus we think that only Greek speaking Cypriots exist. In fact this is exactly what got us into this mess in the first time. Even if the EU takes over and works out a solution, it will still be a compromise plan and then we would perhaps dump them and look for another organisation to adopt us. In a nutshell, the "other" side has claims too and it also deserves the attention of international institutions. The question is will we accept to compromise and share this country with our politically equal Turkish Cypriot community?