Emitter resistor and biasing voltage
The point is to eliminate the need for one resistor. Having said that, I'm not going to argue that this is a good idea.

As you suspect, we assume that \$V_{BE}\$ is relatively constant, which implies that the current through R2 is relatively constant. If we know the current through R1 then we can use KCL to find the base current. Multiply by \$h_{FE}\$ and you have the collector current.

Using this kind of biasing requires very good knowledge of the actual value of \$h_{FE}\$ at the desired bias point....we usually don't have that knowledge in the real world, so adding an emitter resistor helps to compensate for changes in transistor parameters.