Negative prices in the short term are good for consumers if they are a realistic price signal. Not letting the prices go below zero would have a similar effect as not letting the prices go below 5 or 10, you would be hiding information from the system for abitrary reasons. It's really only human psychology that makes the 0 seem more momentous, just as the odomoter ticking over 10000 seems more momentous than the mile before that.

Usually when I've read about negative prices "caused by renewables" it's been the case that there is actually still some non renewable running. The negative price is sending them a signal, namely, that inflexible sources will be penalized more than flexible sources. Someone planning to build a new coal, nuclear or gas plant will take these negative prices into consideration and influence them to prefer more flexible solutions, even if it costs more, because the flexibility will be rewarded (or, equivalently, lack of flexibility will be penalized).