What is the advantages of BPSK+OFDM over usual BPSK (with no OFDM Modulation)?
In a pure AWGN channel there is no benefit from OFDM because the noise will affect the received signal in the same way regardless of whether sent as a higher bandwidth serial stream or lower rate parallel streams. Similarly, there isn't much benefit in a flat fading environment either because, by definition, each constituent stream of the OFDM signal will be affected by the same amplitude change and linear phase shift.

The main benefit from OFDM comes with frequency selective fading. That is because the effects of frequency selective fading worsen as signal bandwidth increases. With OFDM, each parallel low rate signal experiences a flat fading channel instead a frequency selective channel at the full bandwidth - i.e. each individual channel can be represented by a single complex value instead a multi-tap filter. That means frequency selective equalization is easily addressed, which allows us to scale to much higher bandwidths - and everybody wants higher bandwidth.

Note that the question refers to BER only, so other OFDM related characteristics such as spectrum mask or resource allocation are left out.