I totally agree with you OP. However, the EU have only one option left and thats to demand all EU members join the euro. The QE (to the tune of trillions) whilst boosting lending and currency growth short term, only plugs the hole for so long and eventually becomes counter productive with appalling results, which is where we are now.
Romanias playing politics and allegedly seriously considering joining, and I could see Poland getting a canny deal out of joining too. The EU are desperate. I wont be surprised if we see a 'cash for migrants' deal done in the eastern bloc. (Nothing shocking in that, thats exactly what the EU FOM was)
However, the issues will still remain. No matter how they gild this lily, the economics just dont stand up, and you are absolutely right, that attempting to impose a single monetary policy across 28 nations, is utter utter madness. (Especially when member states then just stick 2 fingers up and default)
Germanys holding the financial reins, but whilst the EU may celebrate expanding the eurozone or some small 'win' by averting further short term crises with tax payers bailouts, the citizens paying those bills know further defaults are just around the corner.
Im a leave voter, but Im not celebrating. Those that created this mammoth pyramid scheme, will have their billions safely snaffled away (theyre certainly not holding their investments in euros!), its the man on the street, the honest tax payer who wont be able to secure a competetive mortgage or lending rates. Who sees his pension shrivel to nothing, and unemployment figures soar making the current youth unemployment figures in the eu appear minor.
Its grim times and the EU arent showing any signs of learning any lessons anytime soon.