Tamyrlin wasn't a seat but a ring worn by the leader in the books. They just took the legend about the origin of Amyrlin name and used it in the age of legends. And to be fair it isn't that big of a deal since at that time in the books there were two rival factions, Latra as the leader of one and Lewis as the leader of the other.
In the books the plan to seal the bore was proposed a few times over the course of the war. So people that understood the power might have known the risks if only one side went. That is not diverging from the books so it is again weird to attack the show over it.