Let's suppose the ECB does harmful or blatantly corrupt things and everyone wants to get rid of it. How would you do it? Which elected political body has the power to do that?.
There is no elective body on the European level to do such a thing. Members of the European Parliament have no power to draft a bill, this is reserved for the unelected European Commission. A resolution to abolish the ECB could only be proposed in non-binding form by the European Parliament. The way to get rid of the ECB would be for a national parliament to accept a resolution to leave the currency union.
Well, a national parliament could vote in a resolution to abolish fractional reserve banking and to print receipts tied to physical gold deposits. I wouldn't want to live in that country though.
Why not? Switzerland had a partial backing system until a few years ago. It turned to 100% fiat due to (surprise!) government deficit problems and political pressure from the IMF. As far as I know, Switzerland wasn't an undesirable place to live in when the swiss franc was backed by gold, at least partially. Historically, Switzerland has had one of the most stable financial systems in Europe and one of the best currencies to buy and hold... but that may change since the turn to 100% fiat. The consequences might not be seen in decades.
Well, imagine someone is observing us from Mars. They would see humans busy mining gold from a hole in the ground, then those same humans would put the gold in another hole and hire armed men to guard it. It's pretty dumb to base your economy on this. I think a better policy to safe guard a national currency against devaluation would be to hedge it against an index of commodities and foreign currencies. This way purchasing power would be insured against products and assets you actually need in order to function as an economy.
The point is to back the currency with something physical, to make out-of-thin-air money printing impossible. A basket of metals, or commodities could work too. Under the gold standard you are not basing an economy on it, but the exchange of goods in the economy. That is quite a difference. Compare with the current situation, all exchange is based on paper and numbers in computers. Aliens would say, that is so stupid, anyone including the government can fake that kind of money... By the way, almost all commodities are dug from holes in the ground, if they are not plants or animals.