pulse shaping filter and BER
Why then is the pulse shaping filter not used to filter the sent signal in order to draw the BER curve?

When drawing a BER curve, we're considering the bit or symbol energy.
That energy is the convolution of transmit pulse shape with receive filter evaluated at the symbol instance.
So, that filter is taken into account. We just usually define it such that the pulse energy is 1, and then you don't see it in your equations.