As far as you wondering what use typing speed is to a programmer:
1) if you can type faster, it takes less effort to fix cosmetic mistakes and you do so more often. you must have noticed as well when looking over the shoulder of a slow typer they seem to make more errors? or maybe it just seems more tedious because you're waiting on it. you must have also seen that a really skilled typist can make an error and have it corrected before you hardly notice it (which is because they feel their fingers slipped).
2) in a similar sense, if you type faster, it takes less effort to quickly try something out. just type it out, maybe not even immediately test it, because as you see it on the screen you can more easily reason about it and make corrections before you do. if you type slower, you're more likely to get stuck halfway writing a block of code because you're thinking "wait this isn't right" and start doing proto premature optimization (well, that's my problem, I start thinking about what is the best/most concise/pythonic/readable way to write this code halfway, before I even got the rough structure down. I find it's almost always better to first write down something that works).
3) if you type faster you spend less time writing comments on HN and can get back to programming sooner.
I cannot fathom how people can find the time to actually approach any particular problem at a reasonable depth if it will take them more time to type out the solution than reading and understanding the existing code and determining how to solve the problem. Sure there's code where there's boilerplate, or add a line to a bunch of files, or tons of ways that raw typing speed doesn't play much of a benefit, but when it comes time to type, having to move your hands and look to find the { is akin to a carpenter having to read every label to find the bottle of glue.