EU needs to solve this problem at its roots and put pressure on tax Haven states directly. If that necessitates a reform that gives expanded authority to EU so be it.
I'm not confident that the EU will address this situation, much less solve it. The government in Brussels does not want to be known for challenging domestic tax policy that has existed for years, especially in a post-Brexit era. I could be wrong, and maybe the EU will put pressure on small tax havens in order to give reassurance to working class citizens in larger countries.
That is exactly what they shouldn't do. Firstly, what is the agreed definition of a tax haven, and secondly, which countries belong on that naughty list? Thirdly, when many of those countries are EU members with voting and even veto rights to block such reforms, how exactly do you think the EU is going to put pressure on itself?