Thyristor vs IGBT

I would certainly say that thyristors are indeed extremely robust. Many IGBTs are designed to deliberealy limit the max current they can supply to limit short circuit currents and then allow a slower ("soft") turn off within the 5-10us s/c withstand time. So if you want very high peak to average current rating it may be this deliberate thing that is working against you.

Thyristors are 4-layer devices with two sources of carriers in difference with IGBTs. They operate at higher plasma density than 3-layer transistors and have about half the on-state voltage. Higher plasma density means more charge to remove at turn-off, leading to higher turn-off losses. Most thyristors are line commutated so they operate at line frequency and are, for instance, less applicable to variable speed drives. Gate turn-off thyristors exist: GTOs but more recently IGCTs. They offer the same trade-offs mentioned earlier: lower conduction loss and higher turn-off loss but they can operate independently of line or load frequency. Transistors and particularly IGBTs have very fine features and cannot be made as large chips so many small ones must be paralleled in a package (typically 1cm x 1cm) whereas thyristors can be manufactured as monolithic devices up to 6" in diameter. These issues condition the choice of device as a function of application and power level.

In terms of cylco-converters it is 20 years since I have had anything to do with one of them for high power marine propulsion. It wouldn't surprise me if they are still used for that application and others. If space and weight are not premium then thyristor solutions are certainly have more advantages.

One thing that could maybe be added, is that if you compare a Current Source Inverter (with 6 SCR) to a Voltage Source Inverter (with 6 IGBT), the efficiency of the CSI will be definitely better as the CSI will commutate at the motor phase frequency (10-500 Hz for a BLDC motor, depend number of poles and speed for sure) whereas the IGBT will work at 10-50 KHz (PWM control). So there is approximately no commutation losses for a CSI.

When comparing voltage drop of a SCR and an IGBT, for sure, it can be said there are not big difference. But not for the same price! If you compare voltage drop of a SCR between voltage drop of an IGBT of the same price, then SCR is definitely better.
For medium power range (< 10 kW), SCR driving circuit is something very easy to implement: you just need to apply the gate current (you don't need an accurate voltage control like for an IGBT, or do be sure to put the gate at low impedance at OFF state).
And a last, SCRs are still benefits for motor starters or AC induction motor speed control in industrial segments (especially for fan control).

The likelihood of the SCR turning on immediately after it recovers can be determined from the reapplied dV/dT spec. The two transistor model of the SCR has interconnected pnp and npn transistors. If the reapplied dV/dT is too large, then a current flows through the junction capacitance of the device. If this current exceeds a certain threshold, then the internal regenerative action through the transistors results in the unwanted turn ON of the SCR . The snubber across the SCR is usually designed to limit the reapplied dV/dT and prevent false turn ON of the device.