That was not a stabilization problem per-se, but the companies that had to do the stabilization just didn't although the were being paid for that. Please read the final report.
People didn’t do what they said they’d do: No problem with the system it’s the people that didn’t do what they said they would do.
And no more blackouts because now they are running nuclear 24/7 to keep things stable.
And again, it's not completely Spain's government fault as it obviously came from the EU and their anti-nuclear stance.
And sure, it is a Really Good Idea to contract additional intertia to keep the grid stable. But why shouldn't that be done on the open market? Why pay a fortune for spinning a reactor's turbine at idle load when running a gas peaker plant's turbine at idle works just as well for a fraction of the price?
What does it even mean to "protect the nuclear"? Give them free money for the sake of it? They are already facilities being paid to keep the system in sync, or "protected" as you say, and they are paid very handsomely. But someone got greedy, it seems.
For one year we had to hear that the blackout was to blame on the renewables, and now that the final report is out and places zero blame on the shoulders of the renewables, we couldn't read anything in the newspapers (electric sector is a main supporter of local press through ads or indirect ownership), or we have to read incredible bad blame redirects like "this is on the government for not protecting nuclear".