Quite on the contrary. Unity may be very dangerous. Take the automotive business. There are a couple of manufacturers in Europe, and other brands are imported from Asia and America. The market is very competitive. The manufacturers must put a lot of efforts to improve the quality while keeping costs low. The consumer is king: he or she may choose from many car brands at different price levels.
Imagine there is only one car manufacturer in Europe. Imports are banned or severely restricted. What happens?
Not surprisingly, the hypothetical monopoly corporation—which we may call, e.g., United European Automotive—would be free to set prices at its will. There would be only expensive cars and outrageously expensive ones. Quality and innovation would die out. Why bother with improvements when the monopoly corporation is king and the consumer is serf?
It's the same with government. Luckily, European states compete with each other in prices (tax rates) and in services. The Companies House together with the English law, e.g., is a complex of excellent services that lures foreign businesses to the UK. So is the London City.
Tax rate competition is no less crucial. Imagine that a centralised state emerges in Europe. A European republic with a single capital, single Parliament and a single tax code. What happens?
Rather sooner than later, politicians would raise tax rates in a much faster manner than they normally do. They would feel no pressure to improve the quality of services provided. They would merely tax and spend more to buy votes. Again and again. A united Europe would become a third-world country. Think India.
India is a good example. In the early 1970's, there was a combined marginal tax rate of income as high as 97.75% in India. The exorbitant tax rate was duly passed by the democratically voted members of the Indian Parliament.
Was this sort of taxation auspicious for the country's prosperity? Not quite. With all the due respect to India, its democracy has never worked really well. With democracy like that, people often tend to think about merits of a dictatorship. Quite likely, India would be better off if divided into smaller countries with independent tax rates and free trade, similarly as Europe.
Note that my intention is not to offend an Indian reader who might read this article. The perils of centralisation are universal. India is not the only large country that has had problems with its size.
Just for curiosity, Indian automotive industry used to be a government monopoly, too. For decades, it kept producing one obsolete model, the Hindustan Ambassador. Its production is about to be suspended only now.
This gives you a hint how the democracy of a European republic might look and feel like.
Diversity and Europe of independent states with free trade, is vastly superior to centralisation.