I think it's just rare on a site of any size, that a "webmaster" can do it. I remember when universities had *a* webmaster. My first e-comm site was the Sierra Club bookstore, which was maintained (sort of) by two of us working one afternoon a week. Grey backgrounds. Table layouts. All that stuff.
Flash forward. Maybe 10 years ago, I was at a conference where the guy who ran the UCB or Stanford sites spoke. He had a Drupal multisite install with a couple thousand independent sites running on the Pantheon platform. There was a whole team to help departments maintain their sites, but nobody was a "webmaster." You had content creators and site admins in the departments, sysadmins managing the system but doing no content maintenance, a helper team who could help the departments with their content and layout and so forth.
For most sites of any size, there just isn't a person who "masters" them.
As sites grow in complexity, you have a design team, a UX design team, a FED team, a backend team, a DB team, a devops team, a content strategy team, etc. On a medium site, this is likely to be just 2-3 people total. On a big site, it could be a dozen to hundreds.
At this point, I know very, very few people who do both design and technical stuff. I just did a site without a designer... it came out nice, but it was a lot less efficient and to my eye still has a lot of things a real designer would balk at.
