Two reasons: 1) You could see when the Eureka! moments occur. 2) To easily get a real measure of how long it really takes to write.

I have a real problem with 2), both with underestimating how long it will take to do things I think will be easy to write, and overestimating things I think will be hard. Of course, there's a lot more to writing than typing, but it could provide important information that is tedious to track at a high level and impossible to track at the level of granularity that this app could.

I think (from comment above: "not working all day") you took much longer than the figure above? Perhaps a lot more thought goes into an essay than I imagine?