This is in fact a very good feature. When power is cheap or negative it's because there is more generation than load in some segment of the grid. To fix this you can tell people to stop generating, you can tell people to start loading, or you can just drop the price and let both happen on their own.

There are targetted ways this is done when the difference is so big it threatens grid stability, but its often better to let the market handle the gross imbalance on longer timescales when grid stability is not threatened.

There are some things markets are very good at. This is one of them.

It's actually particularly important that prices be able to go negative in an electricity market, because it's physically impossible to store electricity: it must be generated and consumed at the same moment. "Electricity storage" is shorthand for "conversion to and from a different kind of energy", which from the perspective of the grid is just a kind of consumption or generation. And if there is too much unused power on the grid, it will damage it.

No the opposite is the case. How would you expect a zero minimum price to be enforced? All waste products would have to be disposed by the government for free and the thing is that this costs money. Negative prices signal a desire to get rid of something.