Old Fashioned Half Bridge converter

[Faringdon]

Hi,
The attached is a well known, old fashioned open loop Half Bridge SMPS of 833W output power. (PDF schem and LTspice attached)
It relies on transformer leakage inductance instead of an output inductor. At 107us, there is an enormous shoot-through event due to the top  FET  turning ON, just after the diode of the bottom FET had been conducting. (This is during the startup event, but could also happen in load transients).

Would you agree that this SMPS  really needs SiC type FETs? Eg as follows…
https://fscdn.rohm.com/en/products/databook/datasheet/discrete/sic/mosfet/sct3060al-e.pdf

Would you agree that the following non SiC FET  is unsuitable here? (STW20NB50)…..
https://www.mouser.co.uk/datasheet/2/389/stmicroelectronics_cd00001063-1204680.pdf