Yes but at the moment Russia has huge influence over Ukraine, closer ties (no full membership, it is totally unrealistic in short and medium term) with EU would counterbalance that and actually make them more independent. “Ukraine should stay independent/they should stay away from homo EU” is the line of Putinists and in practice it means “Ukraine should stay under Russian boot”.
Ukraine is a corrupt bankrupt nation on the verge of collapse. This isn't America's problem to fix nor is it an obligation of the American taxpayer to subsidize.
Take your EU begger's bowl elsewhere.