That would never fly anyway. The EU insists on reciprocity — although negotiations can take time. For instance the US is the last non-reciprotal country on the visa-free list.
And EU citizens get their citizenship through the national one, cf Treaty on the Functioning of the European Union Article 20:
> Citizenship of the Union is hereby established. Every person holding the nationality of a Member State shall be a citizen of the Union. Citizenship of the Union shall be additional to and not replace national citizenship.
Of note, EU citizenship is a subset of national citizenship as countries get to decide who is or is not a "national" member.
This distinction is mostly visible for overseas territories e.g. Greenland and the Faroe Islands are both part of the Kingdom of Denmark but both outside the EU, yet Greenlanders are EU Citizens while Faroese are not.