This massively simplifies reality.
E.g. in Finland where I live we also have issues with negative power prices. A few years ago we had some really low prices. It turns out, a fair bit of wind power producers never opted to add to their windmills any remote shutdown possibility, nor did they have the ability to monitor prices and react to them automatically. I.e. they just kept generating no matter the price, and had offers in at the network level at the lowest permissable price.
Since then, when they lost a non-insignifcant amount of money by running at negative prices, they've started installing control electronics in windmills and building IT systems and prediction algorithms to be able to react to this.
In the EU it is not as simple as "turning off when the prices are negative" since producers offer a certain capacity to the grid in an auction system the day before. You have to predict the weather + overall demand and set your offer accordingly.