So the only options remaining for Greece, long term, are to either cede fiscal control as well, or go their own separate way again (grexit) with their own currency.
(But as I said, none of this matter as long as Germany is willing to continue underwriting their debt, which they will continue to do for years, most likely... but not forever.)
Yes, if it ever happens that Germany and France need their economy bailed out in the future they should also have to give up some autonomy.
The European Parliament's power is quite limited in reality, and most of the power is held by the member states and the Commission in practice. It can veto some (but not all) things, but can't even introduce legislation.
And the Eurozone is definitely not democratic, it's run by finance ministers.
Some people like to call undemocratic elections that did not pan out the way they hoped.
There is a parliament, but there's no real pan-European parties. So the parliament is dominated by a center-right and center-left coalition which work together to make up the government. The opposition is largely made up of "fuck the EU" protest parties who pride themselves in not participating in any sort of political affairs. And since the voting is the European tradition of "you vote for the party, not individual members," you tend to have members that toe the party lines (unlike the US political system). The end result is that European elections tend not to be able to effect any change in policy in the European Parliament.
The term I heard used for this is "democratic deficit."
Ceding sovereignty to an undemocratic body.
Wonderful.