"annihilation of" is a perfectly acceptable phrase in written English.
You would use the phrase to describe the destruction or obliteration of something; for example, "the annihilation of the enemy forces".
"The annihilation of the Jews must be the necessary consequence".
Their aim was "the total annihilation of Serbia".
Neither do people calling for the annihilation of their neighbors.
Appropriately, we mourn Adam Lanza's annihilation of others more than his self-annihilation.
When she screamed as a young woman it was "like disembowelling myself", an annihilation of selfhood.
The Teutonic invasions of 1278 83 brought about total annihilation of the indigenous Podlasian tribes.
Diarra played in an Oct. 8 friendly: a 4-0 annihilatiof of Armenia in Nice.
"Never in my memory had they come so close to total annihilation of an author's work".
Only weather and rebel cavalry under Gen. Nathan Bedford Forrest prevented annihilation of Hood's army.
A nature away-day affords a meditative cleansing, the annihilation of self-consciousness.
There was now proof that annihilation of Jews was official German policy.
