The circuit on the left is prone to not starting to oscillate, especially in simulations. The circuit on the right has DC negative feedback, which keeps the transistors out of saturation except right after they switch ON. This allows oscillation to start more readily, especially in simulations.
There are ways of getting the circuit on the left to start in simulation. In practice, it will generally start, due to component mismatches and the startup transients introduced by the power supply turn-on step.
I agree that the circuit on the right is not as useful as the other one. Since the transistors don't saturate, you won't get good logic "0" levels, although there are relatively simple ways to get around this.
I think the circuit on the right was presented as a simulation exercise, and not necessarily as a useful circuit.
There are other types of multivibrators. Google "emitter-coupled multivibrator".