I like to compare a product with a pushcart that many people are pushing, fixing, and loading at the same time. Unfortunately in most cases the end result of such setup is a broken, overloaded product that goes nowhere. While you can concentrate on doing just one thing only for some time, you must eventually do all the three (pushing, fixing, and loading) or you risk coming in a situation where the pushcart is left behind by the customers. Initially the pushcart (i.e. the product) is light, well-oiled, loaded only with essential features, and there are only a handful people pushing it. But as the pushcart matures it gets loaded with new offerings, the wheels wear off, it gets surrounded by customers preventing it from moving, and many more people are pushing the cart and they are not all pushing in the same direction.
As the main role of a product manager I consider pushing things forward. Finding the right direction and getting everybody move along is a full-time job in its own right. If the product managers must fix the cart at the same time or is busy loading the product with new offerings that customers request, he or she will hardly have time to look for bigger opportunities which might await next door. Therefore it is essential that the product organization can rely on engineering to keep the product up and running and on sales organization to sell available offerings. If the engineering cannot keep the product up, the product manager will spend his or her days extinguishing fires and act in retroactive mode. And if the sales engineering bows to every customer request, the product will be pushed around at the whim of customers.