In short-terme I agree with you. But, longterm and in case of Greece: They won't stay in Euro because the simple fact, that they need a "softer currency".
Why? What would that accomplish? Greece doesn't need a softer currency. Greece desperately needs economic growth.
Their economic strenghts is not strong enough. For the next months I think, we will see some compromises on both sides (EU and Greece), because nobody has an interest that Greece leaves the Euro. But in longterm... I don't think they will stay. I don't think Euro will survive the next 10 years. We already see a "tearing dynamic" (don't know if it's the right word) in the EU-population. The next elections of the South-States could bring another parties like Syriza to power. Even germany (I'm from germany) is not immune for more extrem parties.
The trouble with Greece, politically speaking, is not extremists (Syriza aren't extremists, just idiots). It is corruption. Greece scores very badly on this, just like every other country in the Balkan area plus Italy. Unless Syriza manages to come down hard on curruption, there isn't a lot of hope. The rest of the Union is doing alright and most members are doing their best to improve the situation. While it is natural for people to be sceptical of their government in the midst of a downpour, most Europeans (think 60%+) are still in favour of staying with the union. The percentage is even higher amoung the European youth, so there's hope for the future. The real disagreement is not about the union, but about policy.
And: Greece is just earlier than some others. Every state is over-indebted and some others will come to trouble soon. The only antidote are more liabilities and the central bank pumps the market... It's mathematically impossible that this game will end well.
Actually, most Eurozone countries are doing okay with respect to debts. It's important to keep in mind that it's the relative percentages that count, not the nominal amount. Higher debt isn't a problem if your economy can shoulder it. The problem with Greece is that it can't. It imports nearly twice as much as it exports and their government spends a whopping 160% of GDP. The economic troubles of any other EU country pale in comparison. Yes; Italy, Ireland and Portugal are still spending too much, but not as crazy much as Greece.
The central banks aren't 'pumping' the markets, by the way. They are transferring wealth from the people to themselves through financial markets. QE is just a very advanced way of taxation. The net effect is cheaper loans for the governments.