You misunderstand. The Watchers would just be notifying the Kages of the sealing failure, and that they have dealt with those responsible with extreme prejudice. With the responsible parties eliminated and the Kages aware of this, there's not much reason to lash out randomly and start a war.
Imagine that in our world, some scientist releases some kind of mystical quantum virus that stops radio waves working. All equipment reliant on their use just shuts down. It makes no sense. It shouldn't even be possible. A basic piece of human civilisation, one founded in immutable physical laws, is gone forever and now we have to cope.
Now imagine, as a layperson, discovering the further implications. Turns out any quantum physicist can cause this kind of accident, without even needing special equipment. Turns out they've known all along that disasters on this scale are theoretically possible and it hasn't stopped them experimenting. Turns out that the only way to make sure that next time, say, somebody doesn't disable the concept of electricity, is to stop all quantum physics research ever.
Do
you want to be a quantum physicist in that world?
(You can pick apart the details of the analogy, but the basic takeaway point is that suddenly every ninja in the world is discovering that sealing is terrifyingly dangerous, that it is capable of destroying things they didn't even know could be destroyed, and that they have no way to protect themselves except getting rid of all the sealmasters.)
Regarding the Hengrue: would it be viable for this event to be the source of the outbreak of a chakra-infecting virus? One which is rapidly transferred by contact, has an incubation time of <however long it takes all contestants to get back to their villages> and causes henge not to work any more. That would save having to deal with everyone in deep cover suddenly having their disguises stop working.
In its own ways, this is worse than the sealing failure hypothesis. This is just a random effect that follows the patterns of a disease (though every medic-nin in the world will swear that something like this is impossible), arose spontaneously, and could arise spontaneously again at any time, with no known means of prevention or cure. Unless it's actually a bioweapon, and with that entirely reasonable suspicion, cue WW4.
Fundamentally, the reason I support the cognitive retcon version is that I can see no scenario in which one of the Academy Three, the most basic, fundamental techniques that have worked for every single ninja in the world for as long as there has been ninjutsu (as far as anyone knows) can just switch off, and there will not be huge, far-reaching consequences that will completely derail our worldbuilding and plot direction. Meanwhile, the illusiory version solves many of the mechanical problems inherent to the technique, but it retains most of the social ones ("How can a society where everybody can disguise themselves as anybody else at any time even slightly resemble a conventional one?").