Why harmonic components appear only after a certain level when a signal is clipped?
Is this a well-known phenomenon? 


Yes, of course. You will see harmonics as soon as your clip point is lower than the maximum amplitude in the time domain. The latter is a function of the relative phases between the harmonic components. In your case the max amplitude is indeed 2.5 (plus whatever the noise adds).

If you change the phases you will get a different clip point. For example, if you use cosine instead of sine, you will get a clip point of 3.0