Much of the unrest, violence and outright civil war in both England and Scotland during the fifteenth century resulted from the incapacity of a single man, the monarch, to govern effectively, or with wide-spread support. The personality and ability of the individual was paramount in creating a stable political environment, but the principle of inheritance could often result in the King being less competent than was desirable, as in the case of Henry VI in England, or just unpleasant and unpopular, like James III in Scotland.
So, whilst lip-service was paid to primogeniture, if the result were unacceptable, like Richard II or Henry VI, then other options would be chosen. Scotland had a clear line of inheritance from parent to child throughout the century, but the situation in England was far more complex, with succession crises arising in every reign. As Parliament grew stronger, it began to demand involvement in the choice of successor, a claim that Elizabeth resisted to the end of her days.