> Rolling over debt at an interest rate set by the private market is not sustainable. So, the ECB is somewhat trapped.
The issuers roll over debt at their own discretion. The ECB only has the risk of some issuers defaulting before those issuers pay the ECB back in whole, and to offset that risk the ECB limited the universe of eligible assets to as low as a BBB rating. I think it is merely embarrassing for an institution that uses public money to experience defaults, but it is accountable to no one and it creates that public money. It is more like a human-productivity futures contract.
And yes, if the ECB really feels at risk then it can lower the target interest rate deeper negative, and issuers will issue new debt at even more attractive rates since the money is free. Yes, this is your renew QE scenario.
The ECB is not trapped, the private wealth is.
Sure, it is a monetary policy twilight zone, but I think the market tolerance and financial market outcome is not as dire as is often reported. The worries are hyperinflation, but this is a currency term that would be called dilution in other asset classes. Managed dilution of a currency-share is what they are doing. The other worry is balance sheet unwinding, but central banks don't need to do that and can completely distort the market so that their position is profitable anyway (further dilution lowering interest rates so that the issuer can rollover debt instead of defaulting). The last worry is market intolerance to that currency's monetary policy, but the whole world is doing this right now there is nowhere for private money to go except crypto and art.