Look at how India works and its history. The British did not control the whole subcontinent. There were 600 "princely states" running parallelly with many different kinds of agreements with different European colonial powers. Some were small city states and some larger than most countries in the EU. So how did a single federal structure emerge and survive? They have more issues, many more divisions, less resources, and yet have survived a whole lot more chaos the EU ever has. Through out its history the pressure has produced many leaders that don't just have regional influence but pan India influence. The EU hasn't produced such people. It hasn't felt enough pressure to do it yet. So thank Putin and Trump for increasing that pressure.
OTOH, India has elections from almost the very beginning, so there's at least a chance to elect capable leaders. EU, to this day, does not and so far it doesn't seem that Putin/Trump are going to change that.