The problem is that there can be no competition between ebook sellers - the publishers are "price fixing" which is illegal in many jurisdictions.
Under the old system, the ebook sellers (like Amazon, Kobo etc.) had some room within which they could discount books (just like a real store could) - the agency model doesn't allow that.
Notably absent is the publisher "Random House" - they decided against the Agency Model in the UK because they thought it was illegal and didn't want to take the risk.
No, this is not the problem. There is still competition between e-book sellers. It's just that those sellers are the publishers. There is nothing in any country's price-fixing law that required competition to be among *retailers.* Both wholesale systems and agency systems are permissible because they both permit competition on prices.
What most of these investigations focus on (and there have been some in the US as well) is not agency pricing per se, but on the provision in the contracts that don't allow a publisher to sell a book through one retailer for less than it does through another. In other words, while the publisher sets the price and sells it through an agent (Amazon, Apple, B&N) for its price, the contracts with the agents don't permit the publisher to sell a product for less through Amazon than they do through Apple.
It's not clear that these kinds of agreements violate price fixing laws - of the couple of investigations announced by state attorneys general in the US 18 months ago, nothing has seemed to result, so there may be no problem. But as these contracts explicitly mention pricing, it makes sense that someone would investigate.
The other issue that may be being looked at is the fact that all major EU countries except the UK have price maintenance laws that do not permit a retailer to sell a book for less than the price set by the publisher. Even though these are not agency agreements. This means that Amazon in France or Germany, say, can't generally sell a book - even a paper book - for less than the price offered by a B&M bookstore. This is something that the EU might be looking into, although as this is legally required in most large EU members, it's not clear what they could do about it.
This has nothing to do with international rights, either. When an author writes a book, he owns the worldwide rights. He can choose to sell the rights to distribute the book in the US to one company, and the rights to distribute the book in another country to a different company. Thus, when Amazon won't sell you a book because you live in Brazil, it's because the US publisher does not have the right to do so. This is inconvenient in the e-book world. And authors might want to rethink whether this sort of arrangement makes sense for e-books (and it might) - but it's not illegal or wrong.