This is honestly a better solution than what's being offered in popular politics. It does what most people on the right or left fail to do which is after offering a solution; rationalize to what cost and effect the solution is viable, and determine the means of achieving this solution. Where this governor fails is fully rationalizing the practicality of reducing the number of possible exits, which is honestly stupid in the context of a school shooter entering what's theoretically the only exit to the school, trapping thousands of students like pigs at a slaughterhouse. The idea of reducing the number of entrances, though, is not that bad of an idea.
If schools were to limit school entry to one or two entrances and beef up security at those locations, possibly put a check-in-point between outside and the students, I believe a school schooter would have a harder time committing as mass shooting. The school can retain the same amount of exits, ensuring that they're only one-way exits where people can only exit. The only theoretical flaw I see with this solution is the possibility of the school shooter having an accomplice who grants them entry from one of the exits, giving them a golden opportunity to wreak havoc, but that's statistically improbable, seeing as how nothing of the like has happened before. Thinking back to my high school, there were far too many two-way entrances to count; from the auditorium, to the gym, to a north, south, east, and west entrance, to a cafeteria entrance, and even a library entrance, so I personally dont see this solution as being unwarranted.
I'm rewatched this video 5, 8, 10 times now, and even though you framed this as something worthy of mockery, it's honestly not that bad of an idea if refined.
