But you will also, in general, get better at solving simple problems, but those are not the problems you will be dealing with. To put it simply — The complexity of the issues will grow with your skill.

Absolutely and completely true. That feeling of "I have no idea how to solve this" never completely disappears because with more experience comes more expectations. People will come to you with requests for complex systems you've never even heard of, and you have to create a solution. But those problem solving skills you built on the path to senior really come in handy there, and then of course all the time-saving knowledge of knowing all the "gotchas" and what is plausible. Yes, I can easily solve most of the issues that juniors struggle with, but I still wrestle with my own issues semi-regularly.

Another thing people don't often talk about is skill atrophy. As your skill-set grows, the length of time between using skills becomes greater. Programming knowledge fades pretty rapidly. That's compounded by the fact that a decent chunk of your time is now supervisory. So you'll still spend lots of time in the docs, refreshing all that knowledge you worked so hard to acquire.