I'm still not sure what Musha Shukou's point is, but I hope these approach can help.
First, I think the Lock cards are the good example to understand why the multiple puzzle attempts from the single investigator is disabled. It is related to the game speed.
- Of course, as we know, if an investigator fails to unlock a certain door, his movement step is wasted and he cannot move into that room this turn. (Page 8)
If we ignore this rule, each investigator can attempt to unlock a door 3 times. (using Action as Run) Several investigators have Intellect 7, which allows that investigator to use 21 puzzle movements (without skill point), making almost all the puzzle Lock cards useless. Keeper will cry.
Second, I think the MG's special ability and the attempt rule is not related. I think Musha Shukou claims the 'SPECIAL ABILITY' should be above all the rules and ignore any other rule standards against it. But the MG's ability enables 'ADDITIONAL ACTION', and the attempt rule disables 'PUZZLE ATTEMPT', so I think the MG's ability is not against the attempt rule. As Dam described, the investigator will fall into the situation that he explores again, automatically fails the puzzle, and ends his explore action.
Third, if that investigator still wants the MG's ability fully applied, he should consider another choices. Because I play as a Keeper a lot, I always consider Joe Diamond as an investigator who can explore 2 rooms a turn, with Move - Explore - Move - Explore. Run or Attack action can also be a good choice. Even Drop action can be useful, because MG goes upon the explore pile OVER THAT OBSTACLE, and next explorer can get a free action.
In addition, the highest Intellect, Harvey Walters and Kate Winthrop have, is 6~7. Joe has Intellect 5~6. It's high enough!