Why is it important for a router to have a metric for determining an optimal route? would it be workable to run a network without metrics?

It is important that a router has a metric because this value is assigned the IP route and this value is reflected in terms of link speed. It is not feasible, it is necessary to know the values that are assigned in the network, however, there are types of networks that manage to go without this type of value, but it is still an important element in the networks.