this is basically the point of representative democracy!The EU isn't a democracy or even a representative democracy. Notice how lots of people wrote to their MEPs and nothing happened other than MEPs calling their voters stupid? That's because in the EU all decisions are ultimately made by the Commission. The Commission started this, the Commission made it happen and by treaty the Commission is the only body able to actually propose changes to the law.
The EU Parliament quite literally doesn't fit the dictionary definition of Parliament. There isn't any way voters can change this law by voting, not even if every party was for changing it, because even a majority of MEPs cannot change the law. But changing the law is the entire and sole purpose of politicians, so we can observe that MEPs aren't really politicians.
A group elects someone who’s better at statecraft than the group is
That has never been part of the idea of democracy. What makes you think politicians are so great at statecraft? There are no tests they have to pass, assuming you could even make such a test to begin with. What's the definition of statecraft, even?
There's no evidence politicians are smarter or better than the average voter. That's why anyone can turn up and get votes.
Or, from the people’s perspective: elected representatives engage in awful horse-trading and disrespect their constituency’s opinions, and yet gradually everything gets better “somehow.”
For a whole lot of people in the EU things are either stagnant or getting worse. Look at the dire economic performance of Italy since joining the Eurozone: was growing, since flat.
Things don't get better because people repeatedly elect politicians who are superior to themselves. Things, by and large, get better when governments shrink and stay out of things. The fate of the eastern bloc under Soviet rule and then capitalist democratic rule shows that in action (although, now they are at risk of going backwards thanks to things like Article 13).
There are a lot of things you just can’t get done using direct democracy.
Tell that to the Swiss. Most successful country on the continent, by far.