I understand that the Early Church did a lot of work to define a list of books that were to be the standard, and iirc they mostly based it on actual use more than theology, so I guess it was mostly a power struggle among the communities? Afterwards the power was very much centralized though, so why keep four different, and on many points contradictory, accounts of the same story? Why not try and present a single narrative?
Why did the Christian Church never managed (or tried?) to unify the Gospels into a single account?
They did. They're called Gospel harmonies. The most well known and probably oldest of these attempts is called the Diatessaron, from the late second century or so. (The link provided goes to a list of sources and translations of the text.) And to this day, Gospel harmonies are being produced (though now they tend to appear on film more than in text [1]).
So the assumption underlying your question is faulty. That being said, you have an inkling of the answer:
I guess it was mostly a power struggle among the communities
The best way to maintain unity in a far-flung collection of independent and squabbling communities is to incorporate their preferred texts unadulterated into a larger collection of sacred writings.
If you want a more in depth answer to the question you've posed, your best bet is /r/AcademicBiblical.
[1] For example, Gibson's The Passion of the Christ is a harmony of the Passion narratives, since he includes story elements from all four Gospels. And pretty much every Nativity story you see on TV or film is going to be a combination of Matthew and Luke, since the shepherds only appear in Luke and the magi only appear in Matthew.