BER vs SNR measurement in a Digital communication system
In general, what you have shown and said is correct. For a fixed transmission rate \$R\$, a BER vs SNR curve will show you how well the receiver works with changing SNR levels and is arguably one of the best ways too assess overall receiver performance. The SNR value where the BER is \$10^{-9}\$ is usually noted and specified in the transceiver's datasheet as the transceiver receive sensitivity.