Initializing timer registers on 16bit counter?

Anyhow, it only works as it should when WGM10 = 0.

For normal counting mode, you need WGM10 set to 0.

Now the question arises is why WGM10 is not 0, although the datasheet claims the default value for TCCR1A is 0.

Its not in the default normal counting mode because the Arduino startup code initializes the timers for PWM. If you want a particular mode you should always explicitly set all relevant registers.