I agree. Negative prices make perfect sense in electricity markets, and journalism does a bad job at explaining it.
Supply and demand must always be in equilibrium in real time with electricity (forgetting storage / batteries for a second). If there is more supply than demand or vice versa, then you have instability in the grid and can have blackouts. Those electrons have to go somewhere. This is in contrast to virtually any other good where you can store the good in a warehouse and smooth it supply intertemporaly.
Thus, if there is a big drop in demand or it's simply too sunny / windy of a day, there can be too much supply.
To incentivize reducing supply quickly enough, sometimes prices have to go negative. This is in part because some supply simply cannot reduce quickly (e.g. nuclear) and are still happy to operate in zero price situations bc either they have no marginal cost of generation (solar, wind) or the cost of reducing generation and increasing it back up is high (nuclear, coal).
Thus, there simply might not be enough plants that have the characteristics where they can scale down quickly AND have a marginal cost of generation such that they would turn off when prices go to zero (e.g. combined cycle natural gas plants can turn on and off very quickly and don't want to be on when the price falls below the cost of the gas used to generate electricity, but Australia doesn't have enough of them to absorb a supply decrease as prices fall). Alternatively, the subsidies that you mention shift the break even point into negative prices territory.
Either was, negative is needed to incentivize solar and wind to turn off or else there would be a blackout from oversupply.
Thankfully, this all gets solved with energy storage and all the slow, dirty systems that stay on will be priced out by more nimble renewables and rapid energy storage. Bc then that excess supply is stored and arbitraged to higher price times (when the sun isn't shining and wind isn't blowing). Then prices should always be positive (so long as there is available storage). If the storage is full though, prices could again go negative. Without a place to put those electrons, they quickly go from a good to an externality. It's almost like how we'll pay a musician to perform, but if your neighbor is blasting music at 3am. Without someone willing to consume and pay for those electrons, they literally are just causing trouble for all the other electrons that we do want to consume.
It in part why you can't simply just create significant generation and hook it into the grid anywhere without working with the grid operator. AC power, dude. We don't control where those electrons flow directionally. So you adding too much power somewhere can really destabilize the system.