"It's mainly to ensure that while I'm changing something in one place I don't inadvertently screw up a page someplace else that I may forget to check."
It all comes back to design by testing. Personally, my apps use a lot of layouts, views, and helpers so an automated way to check that a change in one place doesn't affect my UI somewhere else is paramount.
The key here is that it's automated. I use continuous integration, and introducing even one human element breaks the flow of quick pushes and updates.
As for sketching out page design, "form follows function." I'm not thinking about the look of the app at all. I'm not a designer, but once my HTML is written I can show a talented designer exactly what they have to work with to create the best UI/U possible. Basically, I'm not a fan of design-driven development.
I wish I could attach an image so you could see where I am with my current project. It's a logo at the top, followed by a list of links, a dropdown, another list of links, some content, etc. One on top of the other, no design at all. Black text, white screen. It is very clear though what the page is suposed to accomplish. Let the designer do their job, and I'll TDD my CSS when I turn their vision into code.