Very important on the research front too just because it gets you on people's radars for symposia speakers, journal reviews and all the other miscellaneous things you have to do as an academic. Not to mention any implicit bias that occurs when reviewing manuscripts or grants for "That nice guy/gal you spoke to at least year's xyz meeting" that we like to pretend doesn't matter....but does.
Not directly relevant to the OP but going to share my thoughts on networking just because I feel like this comes up often on this board. Most of us loathe networking, but I've also found most people (and particularly students) envision it as a much more smarmy and ridiculous process than it actually needs to be. You don't need to go smoke cigars with the dean in the back room of a country club and agree to trade favors for a vote on a key issue at the faculty senate meeting, or go out bar hopping til 3AM at a conference while playing wingman/woman to the sad divorcee trying to pick up someone half their age. We get people here all the time who think that is what networking means. Go to a conference, ask a question at a talk and say "Hi, really enjoyed your talk" if you bump into them at the poster session after. Don't even have to go out of their way to track them down. Rather than waiting for your friend to be done talking to that person you don't know, walk up and say hello, shake hands - pop in a "Just wanted to say hi to Steve, but nice to meet you Sarah" and be on your way. If you really feel like jumping into it, join a committee based in part on who else is currently on it and then be useful. Build a couple habits like these and you're good to go.
Long story short, academic networking is a low bar relative to much of industry. Just being nice and not "Holy **** that person is socially awkward af" level-introverted should be more than enough networking to get by in this field. To succeed as a clinician, you need to have enough social skills that other people do not find you viscerally uncomfortable to be around so you are mostly there. You don't need to be extraverted (few academics are) - just push a little closer to the center on an introversion/extraversion scale and don't be a raging dingus and you're fine.