Why doesn't the smartest person in the world modify their own brain to become smarter in a similar fashion?

Well to some extent smart people do. They do research into how the brain works, how particular sort of drugs affect it, which hormones and neurotransmitters are correlated with what particular phenomenological experiences or behavioural effects, and they take drugs or regulate their diet accordingly. Ray Kurzweil, for instance, is a pretty smart guy who takes something like 150 supplement pills a day.

However, our brains are extremely complex and the tools we have to inspect and modify it are pretty crude. We can't tweak the properties of individual neurons or affect the development of specific dendrites just so. We usually are forced to manipulate our brains through much cruder means like taking drugs that will be distributed throughout our entire brain (but may only affect certain receptors), or transcranial magnetic stimulation. And most of the time the only way we can get feedback about how something like this is affecting the brain is to treat it like a black box and judge its effects based on the behaviour of the individual, or what they report they are experiencing.

Our brains are neural networks with some 80 billion nodes and 750 trillion edges. Our tools for inspecting and manipulating it are crude, and even if we did have much finer tools, the sheer complexity of such a system would overwhelm even the smartest of us.

In comparison, the source code for the first AGI would necessarily have to be developed in such a way that it could be understood by a human mind, and such an AGI could easily change any part of that code (because this is something programs can do today - you could write a program that can modify its own source code, and this is something I've done with a chatbot I developed).

It seems like you're arguing that the brain is a vastly inferior design for intelligence. I just don't see how millions of years of evolution could create that big of a lemon.

I'm not really saying it's a lemon. It's obviously good enough a design to have allowed us to survive and reproduce to the point where we're fucking over most other life on the planet. I'm just saying that our brain and other part of ourselves was, at the end of the day, developed through an unintelligent process, meaning there's a lot of makeshift solutions and redundant garbage. Most of our genome is comprised of junk DNA, after all.

Evolution doesn't come up with perfect solutions; it comes up with adequate solutions. Furthermore, evolution isn't primarily selecting for intelligence; it selects for whatever makes us best at reproducing within our environment, and high intelligence certainly doesn't always result in organisms that can or want to breed (I'm looking at this subreddit and others).

I believe that if the process of developing an intelligent being were intelligently guided (e.g. by AI researchers), we could up with a much better result in a much smaller timeframe. We could identify exactly what it is that allows consciousness to exist, cut out all the extraneous stuff, find out how that can be reproduced artificially, and then choose the materials that have the best properties to replicate a consciousness. And then, understanding how all of it works, we could scale it up. This is just like how progress is made in any other area, from developing better computers to better mobile phones.