1. First, in what situation would a TO witness a squib and decide NOT to take action immediately -- either STOP, or make the firearm safe? And if STOP is called, isn't that run on the stage done? A reshoot is possible if the TO was wrong, of course.
2. Next, per SHB p. 14, if there is a squib, there is no 'check the barrel'. It is 'make the firearm safe and continue with the next firearm'. How would 'check the barrel and let the shooter proceed' look in practice? If you stop the shooter, isn't the stage done? It's not as if you can call 'time out' in the stage to check the barrel.
3. Finally, once the stage is done, removing the offending wad is just a matter of running a rod down the barrel (I have used a car's radio antennae in a pinch). Why continue with an obstructed barrel if it can be cleared?
What would be the logic in allowing a shooter to continue with a gun with a known safety issue? Money's not on the line, we're not defending freedom -- we don't even let people move and shoot at the same time. In letting a shooter continue with one obstructed barrel, you're depending on someone who's shooting routine has been rattled to overcome their established muscle memory and avoid loading the obstructed barrel while they're juggling the sweeps, the shooting order, etc. Some people could handle it, some people who could't. Following the SHB, there is no judgement for who is who.
And if you decide to let the shooter continue with one obstructed barrel, as a TO -- would you stand just as close to the shooter as you normally would?