I rarely have meetings about things are not entirely technical, and I actually enjoy the meetings we have as we always come up with valid points that one alone may not have considered.
Anyway, just wanted to mention my experience as I don't agree that as you become more experienced, you tend to write less code. I am as productive now as I've ever been, even being one of the main and most experienced developers in a team of 20+.
As it comes up here from time to time, I work as a sysadmin, and have my side academic gig, which I'm the solo developer on a serious piece of code. I design, code, test and verify the whole thing, which is immensely satisfying.
My daily job is very connected to my academic gig, and they feed each other. As a result, I can apply what I've learnt from one to the other. We're a small team, doing a lot of big things, hence my work environment is drastically different than yours.
The gist of my comment was actually, "As I get more experienced, I design and write less code because it's more correct from get go. Then I document it at the level needed and I have something concrete and which can be passed over to anyone who wants to maintain or fork it, and this is equally, if not more satisfying".
However, I understand that a project is documentation and future planning, too. So, I want to build an artifact complete with its documentation, which can be sustainably moved forward by anyone other than me.
If I don't document what I've coded, then the joy project becomes a weight on me, and prevents me from moving to new, bigger things. Also, I can show the whole shebang as "I made dis!", and anybody can have an idea what the project is all about.