The other point about knocking off potential claimants - the rival does not need to be imposing, threatening, claiming the throne, or even of age. Witness the case of Lady Jane Grey - all that is necessary is for an ambitious puppet master to get hold of the person with an arguably legitimate claim, to front for their cause. Hence, the more tenuous the current claim, the more important to eliminate roughly equally legitimate rivals.
Someone once pointed out that the real villain of the War of the Roses wasn’t Richard III but Henry VI. Of course if wasn’t Henry’s fault his father died when he was a child or as an adult he had months of mental insanity. But England suffered because of his reign.