An authoritarian right wing government replacing an authoritarian left wing one

[I spent the winter writing songs about getting better]

Why is this so rare? History is full of plenty of examples of an authoritarian right wing government replacing a democratic left wing one (Pinochet, Franco, tons of other coups), an authoritarian right wing government replacing a democratic right wing one (Greek coup and a bunch of others and elected despots consolidating power like Ferdinand Marcos, also depending on your definition of "right wing" could easily apply to things like the Egyptian military seizing power from Mohamed Morsi or most Thai military coups), an authoritarian left wing government replacing an authoritarian right wing one (Cuba, China, Vietnam, Cambodia, just about every communist takeover in Europe, etc.) and a democratic left wing or right wing government replacing an authoritarian right wing one (Portugal and South Africa for left, Greece for right, plenty of other examples in immediate post-war Europe) and a democratic left or right wing government replacing an authoritarian left wing one (see post-communist states.) But an authoritarian right wing one taking over from an authoritarian left wing one is exceedingly rare.

The only examples I can think of Suharto's takeover from Sukarno in Indonesia, and the overthrow of Bela Kun's short lived communist regime in Hungary and replacement with the Miklos Horthy regime. And the latter one is kind of a weak example too since it was basically instigated and installed by external states. Why is this so rare?

[I spent the winter writing songs about getting better]

Russia and Belarus aren't quite examples because the move to authoritarianism was pretty gradual, Russia was a democracy for awhile and even Lukashenko was democratically elected in his first election. The Central Asia republics are interesting cases...but since the leadership was basically the same that's more like the regime just switching orientations instead of being replaced.

I wouldn't really call Allende's government "authoritarian".

I never said it was.

[I spent the winter writing songs about getting better]

Actually another example that just came to mind would be the nationalist governments in the former Yugoslavia.