As title suggested, not every career is heavily based off networking (like real-estate, online marketing, or any info products sales). Yes, networking skills can help, but many careers are skill based and it takes time to sharpening the skill, build up brand for yourself through career movements. Then when you go out there to network it's 10x easier because you actually have value and have the ability or asset to convert those social capital.
FYI: I know this is a more nuanced question. I'm not really asking this for advice for myself. I'm actually more curious about what career folks are in and how are they balancing the two. So for folks commenting on this, if you could also mention what career you are in that will provide some context.