Well, the reason that Eurozone members must show fiscal restraint (i.e. not running deficit above 6% of GDP) is because of the goal of ECB (European Central Bank) is to control inflation period. This is really due to the notion of Goldilocks Economy where the so-called optimal nominal inflation rate should be around 2%.
When governments run high deficits, one of few things must happen. They must increase revenue i.e. increase taxes, they must borrow i.e. issue bonds, or they can print more money i.e. devalue their currency. So besides increase taxes, all of the other measures impacts the nominal interest rate very substantially. By restraining the hands of government to run deficits, EU members would be less tempted to tamper with the currency.
It is impossible for one country to control the interest rate in a currency union even if there are great benefits for it to do so. In a very simple but effective example, say A, B, C are all in a currency union, and similar to the ECB A, B, C all gets to vote on the nominal interest rate by a simple majority. Say country A experinces abnormal economic shocks (disaster, sharp rise in unemployment, big drop off in productivity advantage). Now one of the sensible things the central bank of country A might do when it's not in a currency union is to lower the interest rates to counter act economic downturns. However, say that country B and C are all experiencing inflationary pressures (rising wages, higher consumer prices, etc), by agreeing to raise the interest rate to appease country A would put country B and C between a rock and a hard place.
Of course we have not seen this in the EU yet. Doesn't mean it can't happen. The Euro is still something that works practically but not theoretically. (That doesn't mean that theory isn't right, it just means that the stars are currently aligned correctly for the Eurozone).
There are very convincing macro papers written that says if Michigan can issue it's own currency for the last ten years it would've been a lot better off.