It seems to fall pretty naturally from the theory that any government has a monopoly on the legitimate use of violence[1]. An insurrection would violate that.
The original insurrection was illegal under the old government, but that government no longer exists to prosecute it. The new regime doesn't need to explicitly make insurrection illegal, but it implicitly does through its inherent monopoly on violence.
Democratic countries split the difference by allowing peaceful, scheduled transitions of power. That's not insurrection. Insurrection occurs only when that is violated, especially by violence. Peaceful insurrections are conceivable, but only if the existing government consents to it, which stretches the definition of "insurrection".
[1] https://en.wikipedia.org/wiki/Monopoly_on_violence
