This is a somewhat common practice in various parts of the world. I know several European (both continental and UK) and Canadian banks who do require use of a specific intermediary, and almost all banks in those regions also offer to send money via a specific intermediary. It is allowed in most countries, in fact bank accounts are (generally) not legally required to support international transfers at all.
However this is very rare in the US to the point many people do not even know about it, and many banks either won't support it at all or will need special forms or a manual phone call to perform such a transfer.
In this position you really have a few options I can think of:
- Call the US based bank and see if they have a special procedure to send a wire transfer via a specific intermediary, this will possibly cause them to charge higher fees for the service or they may say no.
- Send the money to a trusted person in Europe who has a bank which does not require a specific intermediary, but supports USD balances. They can then send it on either via another wire or a conventional transfer.
- Use a dedicated international money transfer company like transferwise. They have a guide on how to send USD to accounts outside the US here. Most of these services can cope with the quirks of banks and their transfer requirements, and will at least be a point of contact if there are issues.
(Please note I am not affiliated with any money transfer services or banks, I am just speaking from personal experience using them.)