Your electrician is correct.
What in the world are you doing with "all my dedicated audio lines"? You should have one. ONE!
But hey, don't take my word for it. Who am I? How about Mikey then?
Skip to 15:50 for Fremer's advice on dedicated lines.
https://ultimist.com/video/2018/07/21/michael-fremers-listening-room/So absolutely do not bother. BUT if you are like a lot of guys and really, really, REALLY stubborn especially when it comes to learning, then you STILL do not need another breaker box. Because you can keep all your unnecessary lines and still add more simply by swapping a few existing breakers out for thin twins. These are what they sound like, breakers that take up half the space. Surprised your electrician didn't tell you this.
Well no not really. After 30 years I am no longer surprised to find I know more than the electricians.
2. Would a larger capacity box provide me with a better supply of current that would, in turn, improve my dedicated audio lines?
No. Not even. A larger box is a larger box. It will have a bigger main breaker, yes. But you really should step away from the keyboard and go have a look inside there. It won't kill you to look. Honest.
Does it look like the panel is going to have a bigger wire coming into it? Or are you going to have them change the cable from the pole to the meter to the panel? While you're at it, about that meter...
Reality check. Hope its been useful.