Surely that is harsh.
If the tires blew on landing, the runout was completed on the rims.
Given that, I don't see the taxi as posing an additional risk.
It would be very helpful to hear the opinions of those who have had such an experience.
Upon vacating the runway the pilot has no idea where the FOD from the tyres went if they blew on landing. This kind of FOD has punctured fuel tanks / lines in previous accidents. Add the high temps on the gear-leg from the friction and you have a potential catastrophic fire.
Vacate the runway...maybe, taxi to the gate...absolutely not.