The reason is that classical grids are mostly self-correcting. Rotating inertia can stabilize frequency and can produce or absorb reactive power.
"Reactive power" sounds fancy, but it just means that motors can create a drag. The power lines are giant capacitors, and capacitors have the lowest effective resistance when they are discharged. So the current is greatest when the voltage crosses the zero mark. Inductive (rotating) loads are the opposite, their effective resistance is greatest when the current starts to rise or fall. So this limits the initial inrush of the current.
But there's more! When you have a transformer and a long line, you can essentially get a boost converter. The voltage from a transformer travels through a low-resistance wire until it reaches the end, and because the line can be modeled as a series of capacitors, you essentially get a "charge pump" ( https://en.wikipedia.org/wiki/Charge_pump ). From the viewpoint of the generator you have one large capacitor, but from the viewpoint of a consumer in the middle of the line, you have two capacitors in series.
As a result, the voltage in power lines can _spike_ if there's not enough rotating load. This is called Ferranti effect, and in Spain it was the primary reason for the faults.
This is all fixable, but it requires investment and regulation. And Spain (and other countries) have been neglecting that, by incentivizing the cheapest possible generation.