This has many drawbacks, not least that it disrupts monetary policy transmission, makes banks more exposed to country-specific shocks, and encourages home bias in government bond purchases that strengthen the bank-sovereign loop.
To give an example of how far short we remain of a fully integrated financial market, a recent study found that, between 2005 and 2012, the average number of bank mergers and acquisitions per year in the United States was 343, whereas in Europe the yearly average was just 58.