While your idea has merit, the EU will never go for it.
The main reason why is that countries like Spain, Portugal, Ireland and Greece have received HUGE amounts of infrastructure aid from the EU, much much more than they paid to the EU. These funds (mostly for highways, high speed rail lines, port infrastructure) were supposed to level the playing field between countries like German and The Netherlands (note I am purposely leaving out France here) and the rest of the EU. They also paid for education, electrification, and most anything you might think of.
Several countries, now that they had highways, had to totally change their driving license laws (like Ireland, where you can’t just have a learner permit for 50 years anymore) or at least modify them (in Spain, cars under a certain engine displacement, motorcycles, etc, don’t need a road test to drive, just a knowledge test).
In much of Europe there are more local airports with major scheduled flights than you can imagine (though many are seasonal), in fact there are several major airports (think maybe something the size of Denver Intl) which were paid for by these funds, and you guessed it, government debt, which never even opened despite being 1-2 years old because there is just no demand (also of course the type of air traffic which they were to cater to fell over the last few years).
Obviously this has not worked out the way it was supposed to, and as one might guess, lead to huge inefficiencies rather than paving the way to greater productivity. As more countries joined the EU from eastern Europe, the formula cut off the cash spigot essentially just before the financial crisis.
Why did I leave France out? Well, France needs no infrastructure aid, i’ts modern and relatively clean, minus a bit of radioactivity. However, the vast majority of EU money goes into agriculture subsidies, of which the major share gores to France, of which the major share goes into sugar production (from beets of course). The result is French beet sugar would be much cheaper in Brazil (if they chose to import it) than Brazilian cane sugar.
Well, that how it goes whenever an entity, be it a national government, a provincial government or a local school board gets to spend money that they aren’t responsible for raising through taxes.