For actual writing, a laptop screen is plenty big enough, and many people enjoy the flexibility a laptop allows to write in places other than the desk (in bed, on the couch, in a coffee shop, etc.)
A big screen is most useful to a writer for tasks where you want more than one document open and visible, e.g. comparing drafts or referencing research material. Some people need this more than others. Needing a big screen doesn't mean you need a desktop computer - you can connect a laptop to a big monitor easily enough when you want.
Another point to consider: laptops tend to be more fragile than desktops, with a shorter life expectancy. That's largely because (a) parts have to be made smaller and lighter to fit into a laptop's case and (b) you're moving it around all the time, not always gently. Conversely, you get more oomph for your buck with a desktop, for the same reason.
Me, I have a 20" iMac on my desk, but I do most of my writing these days on a 13" Macbook Air.