Based on the word Europe being in the name. Brexiters are quite petty.
When people imagine a more politically integrated EU, I bet they don't imagine that government run by whoever they consider the kookiest people in the body politic. Imagine that EU integration proceeded apace, and Duda, or Orban, or Johnson became the popularly-elected President of the EU. (The current EU executive structure would never be adequate, of course, in a more politically integrated future.)
Federalism, in principle, is no bad thing - but it should keep to regulation and overarching legislation while letting states largely self govern (i.e. the EU model) rather than top-down tactical governance, which is where the US has ended up.
Ultimately, it’s a question of identity. Americans call themselves Americans. Europeans call themselves French, Dutch, Greek. That shared identity is the key to preventing war - everything else is just a means to that end.
The US couldn’t maintain federalism, and the EU will ultimately end up in the same place. There is no additional structural protection in the EU, there just hasn’t been enough time to erode the sovereignty of the individual member states yet. In some respects, the EU is actually structurally worse. For example, the EU has no equivalent to our anti-Commandeering principle, so the central government can force the member states to execute EU legislation using the apparatus of the domestic governments.