1/3 All states do not invariably dissolve, specifically the bourgeois state. It will maintain its power over people indefinitely if not challenged. The inherent traits that capitalism perpetuates (greed, selfishness, competition) causes the capitalist ruling class to consistently do everything in their power to maintain their power, whether it be reforms to quell the revolutionary masses or fascism to force them into submission.
2/3 A socialist state, on the other hand, can dissolve due to socialism being capable of eliminating the class strife in society by putting power on a more equal level, and since states only exist for one class to maintain supremacy over another, it is possible for a socialist state to dissolve. But a capitalist state will not dissolve of its own accord. It will have to be overthrown by force.
3/3 Also, I'm not confident that your proclamation that anarchism is incompatible with overthrowing the state is accurate, since anarchism is simply the belief that there should be no state or hierarchy, which is compatible with a desire or movement to overthrow the state.
@Radical_EgoCom
In some other threads you mention logic and proof. We can state, by definition, that anarchism implies no state, and therefore overthrowing one government and installing another is not anarchy.
When we discuss history we have left the realms of deduction and induction. That's fine, but let's not pretend rigor.
So far, we have no evidence of overthrow resulting in anarchy. That doesn't make it impossible, but history suggests overthrow results in a new state and a new elite.