Don't worry, the only thing governments will learn from this is that they need to exert even more control. They'll use this as a convenient excuse to centralize the age verification in the interest of security, which conveniently gives the government the final say over which web services you're allowed to use.
The stricter the dictatorship is, the more likely people will resist the regime.
That's why many of the traditional totalitarian regimes are populistic, they do what their people want them to do or what they can convince them is good for them. New Western hybrid regimes still didn't realize they can't rule against their own people forever.
I hope this incident and future data breaches will finally raise awareness of which direction many regimes are going.