France is currently developing La Suite numérique[1], which includes email based on Open-Xchange. The German federal government also proposes Open-Xchange in their openDesk suite[2].
[1] https://lasuite.numerique.gouv.fr/ [2] https://www.opendesk.eu/en/product#email
Why would we even want that, the whole point is to break the monoculture and single vendor dependency not to create an new mostly irrelevant one to be stuffed with has-been and rejects from the national levels the way most of EU's big prestige projects end up being run.
One of the thing that sets EU apart from most federations is that it kind of enables a lot more regional independence in how things are actually implemented while still guaranteeing the rights of the individual citizens, this lead to a lot of dynamism at the local level despite the failings of the central level, and allow this kind of projects to succeed and create paths for others to follow at their own pace.
On one hand, yes. There should be a good EU-wide easy to adopt system.
On the other hand, the more people are involved, the slower progress is. And It makes sense to accelerate nationally and then combine EU-wide later on.
Another missed opportunity to make a EU-wide project.