As some others mentioned, the main benefit of MD is that it provides a specification for developers to follow. I'm not the most creative person in the world, and though I do both front and back end development, I find that the majority of my time is always spent on the "look and feel" of my applications rather than the back-end business logic.
Add to the fact that many people use Android, thus are already familiar with MD.
As also mentioned, mobile devices are becoming more prevalent for common web usage. I find myself often whipping out my phone to either look something up or use some web site. I get really annoyed when I go to a website on my phone and I can't do something because they didn't design the site with mobile in mind...I then have to jump on my laptop to accomplish the task.
If I want to avoid that same annoyance with my own users, I should ensure that mobile design is built into my web applications from the beginning.
On a practical standpoint, I prefer responsive mobile-first design because I then have 1 codebase to maintain instead of both mobile and desktop versions of the site.
In the particular field I write software in, many of my customers are using web applications and technologies that look like they came from the 90s. But they use them because they get their work accomplished.
The focus of developers (and software in general) is first to accomplish the task and provide value, and second to look pretty while doing it (but I do argue that the look/feel does play into the usability). Usability and "prettiness" are not opposites, and MD provides a realistic demonstration of that fact.
Does MD "work" for web applications? Yes, it can. Combined with responsive mobile-first design, I think MD is a great starting point for a developer who isn't as creative himself.