If US banks had the same reporting requirements to EU countries regarding EU dual citizens accounts, this absurd situations of being denied banking relationships in the country you work and reside would stop promptly.
US banks wouldn’t. The reason that the EU is wary of ending up on the USA’s bad side, is that European banks rely on large New York banks for clearing international transfers. They can’t not do business with the USA. American banks don’t have the same dependency on the EU.
Many countries would need information flow about their former or current tax residents to enforce tax obligations, similar to the information the EU banks report to the IRS about US persons. E.g. several EU countries have an exit tax on worldwide income and they would need the reporting from US banks to enforce it.
At the point this is also a competitivity issue for the EU to attract talent and capital. Coming to the EU after having been a US person (citizen or green card) is such a hassle for banking and to manage stock investments in the $100,000s. Just so much pain in terms of paperwork and tax uncertainty that staying in the US and not coming back to the EU solves a lot of hassle.