I do the same, but somewhat differently. The primary reason is that I only accept connections to people I have personally met and interacted with. (The few exceptions to that rule are people whom I've had extensive online dealings with.) The network information tells me who is likely to know more, and more importantly, could probably help to skirt the "Great Wall of HR" by introducing me personally with the people doing the actual hiring. Outside LinkedIn.

When someone in my personal network pings the hiring manager and asks if they can connect me with them, I'm already ahead of the rest. Even if the response is to send the application in through the regular channels, the hiring manager now knows to expect my application. And perhaps most importantly, they know that I have been already vetted for fit and sanity by a person in their personal network. I can refer to that link in the application cover, and help it stand out even further.

The in-system introductions at LinkedIn I consider worthless. Use those, and you get flagged as someone just clicking buttons.

Networking is crucial on any creative field. But if you're willing to artificially "enhance" your network, you're just devalueing that very network - and by extension, yourself. The only things that really matter are the personal connections. They are the ones that can help you - and the ones that you are willing to help yourself.