It should. That's why I'm a Eurofederalist.
The different languages don't matter when more and more we all speak English anyway. Not to mention have translation software. Not to mention that the problem is overstated to begin with. People with different languages can live just fine in the same country, especially when it's divided geographically and you have local control over things to which they are relevant like education.
Despite the rise in the far right they are still a minority basically everwhere and pro-EU sentiment is strong almost across the board.
On a political level the incentives are also there. Plus, we have common enemies and an America pulling back.
The cultural differences are severely overstated. We still mostly believe in the same basics and I bet I have more in common with a left-winger from a different EU country than a right-winger of my own as far as values go. Yet we live in tje same country. Not to mention cultural differences only really matter for unification when they have a political dimension and not all do (like food preferences) and over time many that do, like gay rights, will shift to come together anyway.
Many people talk about these "differences" but I have yet to see a single person list them and explain how they prevent unification or are greater than the differences that already exist within European countries or overshadow the similarities.
We have a lot more in common than what divides us. Especially geopolitically, but also in basic values, mutual support and interdependence.
Not to mention geopolitically europe either unites or becomes an irrelevant backwater.
I'll end on this cuz I'm in bed and falling asleep: A united Europe is not found. You don't just look at what is and determine whether it can be jammed together. A united Europe is built. With effort, compromise and intelligence. And it can be built for the benefit of all Europeans.