They should do it because elected officials will sign it into law. It will be signed into law because people asked for it. People asked for it because they benefit from it. People benefit from it because they need stuff the government pays for.
There is no reason to sympathize with governments that depend on clever paperwork for their nation's success because that is not a tangible good. There is every reason to sympathize with governments that are trying to raise money to invest in their citizens because that is a tangible good.
Eliminating tax havens is no more objectionable than closing an account with a bank that has lost your trust. The bank will adapt and learn as it always does.