> It's not hard to notice whether an element has focused
That's not true for many websites. Maybe you're not using them, but in that case accept that others do.
> and especially if you know you have flaky hardware
We all have flaky hardware. It's called human body :) Sometimes your touchpad press will not register, whatever the computer hardware.
> It's seriously not hard to see where the focus is.
If you're using only websites where it's true, great. First example off the top of my head where it's not true: https://www.anz.com/INETBANK/bankmain.asp - start typing anything in the login box - you'll lose the focus or the page will reload after ~10 seconds. It's one example, but there's lots of similar ones. Another fun one is on a page (not linking, because account is required) where the text boxes for credit card will automatically skip forward every 4 digits, but when you backspace they'll just lose focus instead of skipping back.
> You're implying that the computer somehow magically (telepathically?) determines exactly where your input is to go.
No, that's not it. I'm saying that if I do actions that should put me in a specific mode, a good design does two things: 1) makes it trivial to notice that it happened and 2) minimises the errors if it didn't. Since point 1 is up to the website (and often the mode is not explicit at all), the browser can only handle point 2.
> That's like saying "I don't always look at where I'm going when I drive. Why do I keep crashing into things?"
Here's a large group of people you're missing: people working on a remote desktop with the server not in the same building. This for example includes a lot of government and healthcare offices. If they had to wait for local response for every single character they typed, rather than assume the input mode doesn't randomly change, they wouldn't be able to do their jobs. (on time)