Somebody has to go and turn it off, and having this person available overwhelms all of your operational costs.
Or alternatively, you need the infrastructure to do it automatically, what is currently expensive. (But there aren't intrinsic reasons for that being expensive, it's probably due to lack of scale.)
If it's just slightly negative, or just rarely so, it's not worth it.
There is not “person” turning things on and off.
By making the price go negative, you are creating the market incentives for someone to do something about it: households will invest in BES systems to suck up all that free electricity to use during peak times, and some industrious entrepreneurs might even be convinced to do it on a very large scale to start arbitraging on the price fluctuations.
You don't even need the price to go negative to have a BESS buffer make financial sense.
Prices have gone negative because of things like subsidies - which in the short term is a good thing IMHO - it subsidizes industries developing systems to make use of that free (but not negative cost) energy...