Even if we get 100% of the UK public to vote for say Labour they could still have their views completely ignored if a majority of other nations have voted in right of centre governments (or vice versa). Doesn't sound like an improvement on the UK system to me.
It doesn't have to improve on the UK system it's a separate and different system. If the UK is outvoted in the EU parliament then that too is democratic. It's like the SNP complaining that Scotland didn't vote for something in Westminster. We may not like it but it doesn't have zero legitimacy.