Be careful with this line of thinking. This reads like overcorrection. Like when a nerd realizes they need to learn to network and become obsessed with all aspects of socialization. You can damage your technical excellence through neglect! If you overcorrect and let your technical excellence suffer because you prioritize people too much, then people will like you but not care as much about what you do. They will be less likely to want you in their professional network. ie they like you but don’t respect you.
It all matters, your product or service is only as good as the weakest aspect. Making an offering great means constantly putting your attention on anything falling behind to ensure excellence in all categories that matter.
I like this line of thought. Growing up, I was bombarded with "networking is everything!", "99% of jobs come from connections!", and it was really stressful for me because I'm really terrible at networking and I know it. Felt like I'll never get a job. But guess what? It turns out being freakishly obsessed with something makes you good at it, and being good at something is also a really good way to find a job. All of my engineering jobs thus far were cold contacts with a strong portfolio. Didn't need the network after all.
(that said, of course networking is still effective. it's just, as you said, people overcorrect - even in their advice!)
Being good at your job will only get you so far in a career. As you move up the ladder, social skills become more important to your career. Also, as you get older you will see that networking will be the primary way to get a job. Being good is not enough all the time. Companies need a job to be done they don't really care that you can build a computer or whatever from scratch or whatever merit you want to name that's outside their needs. If they have X candidates to pick from they will gravitate towards the one that can do the job and the one they have some kind of personal connection with -also known as networking.
It's not really about networking. Being able to schmooze is a nice add-on, but it's much more about being able to understand users and teammates. Those are the people you need to think about every day.
It all matters, your product or service is only as good as the weakest aspect. Making an offering great means constantly putting your attention on anything falling behind to ensure excellence in all categories that matter.