After trying some tasks without using the mouse, and with a screen reader (and not being able to see the screen) I'm going to try the same tasks, but with JavaScript turned off.

Task 1: Gmail

Find a starred email in Gmail, go to the link within it, read the article in the link, then unstar the email and return to the inbox

I had to use this in HTML view, which looks very old school. Keyboard shortcuts don't work, which threw me for a moment because I'm so used to using them with Gmail. But otherwise, it was fine, everything worked as expected.

Task 2: YouTube

Find my watch later list, watch a video on it that's not last on the list, look at the comments, then remove it from the watch later list

I didn't get very far with this because it doesn't work. I had a lot of grey circles and rectangles where videos would be. But nothing else. Not even any links. Or an option to view an HTML version of the site.

Task 3: BBC iPlayer

Go to the BBC iPlayer, search for Click and play the most recent episode.

The iPlayer looks almost identical without JavaScript. The only problem I encountered was when I had selected a video to play. It told me I needed JavaScript enabled and greyed out any video actions, and there was no play button.

Conclusion

When the YouTube website didn't work I thought that was probably not unreasonable. The times when you might be surfing with effectively no JS is when you're on a slow connection. And if that's the case then you'd assume that a YouTube video would take so long to download that you just wouldn't bother.

And then the BBC iPlayer site working made that seem more unreasonable. Okay, so I can't play videos, download them or add them to my list, but at least I can see what's there, unlike on YouTube.