I am an engineer, and I rely heavily on metrics, because my job requires quantifying that a system is working correctly. It is impossible to do that correctly without metrics.
Similarly, managing a product team is also managing a running system; that system is just made up of meat sacks whacking plastic buttons with their bony protrusions, rather than computers humming away in data centers. A product manager still needs to quantify that the system making that product is working correctly, and metrics are essential. Otherwise you will only be guessing as to how the system is working, and those guesses will be much more haphazard as the system grows.
Similarly, managing a product team is also managing a running system; that system is just made up of meat sacks whacking plastic buttons with their bony protrusions, rather than computers humming away in data centers. A product manager still needs to quantify that the system making that product is working correctly, and metrics are essential. Otherwise you will only be guessing as to how the system is working, and those guesses will be much more haphazard as the system grows.