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Yep all that.
Bear in mind however though that it's not just the fault of the EU as a whole... people keep voting for the local Tories, like the Dutch VVD, which means people put forward for EU positions are mates of the local Tories and nothing gets fixed.
Ironically, a side-effect of the single market competition rules of the EU are that hard to control companies like Apple and so on are facing opposition...tax evasion is now also under the magnifier.
Once again, the problem with the EU isn't the EU. It's problems such as that Germany wants to disguise its immense internal economic problems (e.g., depressed demand owing to deeply unjust social policies over decades) by export, export, export, and therefore wanted a rushed introduction of the €uro. Or take Juncker turning Luxembourg into a tax haven (he denies any knowledge of this, of course, not hugely convincingly considering he was finance minister and prime minister). I'm pretty sure that if the Euro hadn't been introduced when it was, perception of the EU wouldn't be so skewed, especially in its treatment of the smaller countries less able to benefit from export markets. Schäuble's bullying of Greece was extremely stupid and a huge mistake (not that everything was rosy in Greece, and the reported corruption there certainly can't be allowed to continue, but that could have been addressed in a different way). And so on.
The problem with larger markets is that you tend to get fewer large influences dominating the market, e.g. large European corporations. While a single market is not a bad thing in itself, the way people use it is usually concerning. It's a twisted thing; on the one hand, many people want to work less, so improving productivity is a good thing. On the other hand, social integration, positioning, respect, and economic well-being are all somehow linked to work, so merely improving productivity, with its usual consequence of centralising economic power, doesn't work. You also need a clear understanding that, for instance, someone caring for a disabled elderly relative is doing important work and ought to be rewarded well for that (always difficult to relate work within the family, e.g. housework, to pay, but I think it's just a question of normalising it). If you don't take such steps, greater efficiency will just cause more social cruelty and cause such problems that public funding can't cope, e.g. if ever greater levels of unhappiness and illness are caused.
I'm absolutely certain that the European single market has had similar social consequences to the existing large market in the US, i.e. high levels of poverty, from the Paris banlieue to the North of England, but this depends to a large extent on the fact that it was pushed and promoted very much by right-wing governments in the larger European countries, e.g. Thatcher's, and when the political pendulum had swung back to require corrections, you got Blair and the hapless Blairites like Schröder and Jospin, who for whatever reason (misconceptions or having been co-opted before they ever reached office) didn't push hard enough to restore confidence in the economic system.
Anyway, blah, blah, tl;dr, reforming the EU is undoubtedly the best way of going about it.