On the other hand a Eurozone member cannot set it's own interest rates, inflation, can't restructure it's own debt, doesn't control it's exchange rates etc. It takes away nearly all the financial tools a country has.

Do you know why you need to bail out Ireland? because it doesn't have access to these tools, It can't restructure it's own debt and it can't control it's own currency and exchange rates to settle it and any changes to the Euro which might be a net positive to Ireland would be global and could often result in a net negative to other Eurozone members like Germany.

Lets take exchange rates for or example.

They have the same exchange rate which means that if Ireland and Germany want to export potatoes they both get paid at the same rate in their local currency.

This is a huge deal because it prevents one country from being more competitive than another as it would lose too much on the exchange rates.

This essentially takes away an important tool that countries have which is being competitive on export by reducing their prices but maintaining a good local revenue through favorable exchange rates.

And while it might appear "fair" it's not because fixed exchange rates favor larger economies like Germany which can be competitive more competitive due to simply their sheer production capacity.

Next you have imports again the exchange rate is fixed, also the import taxes are fixed so importing goods into Ireland would cost as much as to Germany excluding other marginal costs which again is a problem because Germany is a larger market, it's closer to the Netherlands which is the major port into the EU, it's on the mainland which give it easier access to the med as well as a land route to Russia, Turkey and beyond.

Now lets look at another example debt restructuring.

Lets look at both "internal" and "external" debt, in this regard internal means in your own local currency and external means in a foreign currency.

Internal debt you can repay by well simply "printing more money", sure you can't go wild with that but this is something all countries do all the time they play with interest rates and many other levers and reduce their debt at the expense of higher short term inflation.

External debt again if you control the exchange rates and control the supply of your own currency you have much better tools for debt restructuring.

And these are just the most crude and basic examples there are benefits to the Eurozone but you do take away most of not all of the tools countries have of managing their own financial and monetary policy. You also cannot make adjustments that you could make otherwise because you now have to set a unified policy across all member countries.