Can a thyristor regain its forward/reverse blocking capability if the current through it is "instantly" brought to zero?
Turn-off time of a thyristor is of the order of microseconds to hundreds of microseconds depending on the type. That's a long way from instantaneous.
Eg. this 40A SCR has a tq of 35us.
You can apply a reverse voltage to reverse blocking thyristors (eg. SCRs) to sweep the carriers out more quickly.