I most certainly don’t write faster than I type, and sending an email or a chat message certainly doesn’t take longer than finding something to write with and something to write on. There is a big factor of habit and lifestyle - I don’t usually write stuff down, so I don’t have prepared/assigned tools for that, but I use my computer a lot, so I do have software installed and tools/commands memorised.
And, frankly, out of many possible options, plain text is something computers are really good at - there’s basically no risk of running out of space, it’s indexable and searchable, it’s editable, and it’s very universal.
Things do get a bit more complex when you include formatting, and a lot more complicated when you start adding annotations or illustrations, or even just more freeform writing styles, but there’s still a major factor of habit - I don’t know what my note taking would look like if I had a habit of pen and paper, but I know I’m very comfortable with using tech for that, and it works great for me!
I think if you tried to spend hours in there the water would go cold, but it’s comfortable for, say, 20, 30, maybe 40 minutes, which is enough to read for a bit or watch an episode of a series. It’s indulgent, but it feels relaxing to shut yourself in the bathroom, go into a tub of hot water and relax isolated from the world outside.