My hypothesis for this is that Less Wrong selects for a portion of people who are looking to jump-start their productivity to a new level of lifestyle, but mostly selects for intelligent but complacent nerds who want to learn to think about arguments better, and like reading blogs.

Any blog selects for people who like reading blogs. :D

LW is about... let's make it a simple slogan... improving your life through better thinking in a community.

Which is like your hypothesis, with the detail that those nerds want to experience a supportive environment. Specifically, an environment that will support them in correct thinking (as opposed to: "you just have to think positively, imagine a lot of success, and the universe will send it to you" or: "don't think about it too much, join this get-rich-quickly scheme"), and in their clumsy attempts at improving the productivity (neither: "just be yourself, relax, learn to accept your situation", nor: "too much talk and no action, either show me some amazing results right now or shut up").

I want to write about the stuff I know ... I will need to study better the topics which I care about

Same here. I would like to write about education in general, and math education specifically. But to make it better than just random opinions, random memories, and random links to "Scenes From The Battleground", I need to read some more materials and gather information.