So does the EU. MEPs are elected just as democratically as MPs (in the UK), Representatives/Senators (in the US), etc.
Magna Carta was about the balance of power between the king and the barons; commoners' interests come into it only incidentally.
The American Revolution is a slightly better case, but note that its "No taxation without representation!" battle-cry wouldn't be any sort of case against the EU because (1) everyone in EU countries does have respresentation, and (2) while for some countries EU membership is a net cost (at least if you ignore the benefits of free trade, free movement, etc.) that cost is a tiny fraction of those countries' total revenue base; e.g., the UK's net contribution is about £8B/year, which is a little over 1% of total UK taxes.
Magna Carta was about the balance of power between the king and the barons; commoners' interests come into it only incidentally.
The American Revolution is a slightly better case, but note that its "No taxation without representation!" battle-cry wouldn't be any sort of case against the EU because (1) everyone in EU countries does have respresentation, and (2) while for some countries EU membership is a net cost (at least if you ignore the benefits of free trade, free movement, etc.) that cost is a tiny fraction of those countries' total revenue base; e.g., the UK's net contribution is about £8B/year, which is a little over 1% of total UK taxes.