First, it allows a single gain stage with both voltage and current gain, and having
a high input impedance and low output impedance without a feedback loop or
degeneration.
Second, this character allows “working the load-line”, the particular description
of the path of the gain device through the voltage/current region in the course of
amplifying into the loudspeaker. By choosing this line wisely, you can achieve
intrinsically lower distortion. Pentodes and Mosfets aren't very good at this.
Third - like Triodes, SITs have a soft overload characteristic. When over-driven
on peaks they present compressed, rounded waveforms instead of sharp
clipping, the result being that they are more graceful under pressure.