The difference in per-capita GDP between the poorest and wealthiest US states is small compared to EU nations. I did some quick research:
Luxembourg GDP Per Capita: 114,370
Ireland GDP Per Capita: 83,990
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Romania GDP Per Capita: 12,510
Bulgaria GDP Per Capita: 9,850
vs:
New York GDP Per Capita: 93,463
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Mississippi GDP Per Capita: 42,411
Yes, NY transfers wealth to Mississippi but the scale of transfer and the relative number of wealthy states vs poor (there's like 5 in the deep south) means the dynamic is completely different. Without significant development in ex-Soviet states I'm not sure how the EU can hold together longterm.