This is definitely the more proactive method of landing an internship. But the more successful interns I have worked with all had an idea what they wanted and they went straight for it.
I tend to think I work really hard and efficiently as possible, so I like to help in what ways I can. Since I'm looking for an internship now, I figured I could apply to companies that had a dire need for interns.
The win-win scenario is that the company gets the help, and I get the experience (obviously).
On the side I've been learning/working on some web development. Most of my experience in that has come from building my website using Jekyll and some node stuff here and there.
I learn fast (fast enough to be useful) so throwing something new at me is a familiar and welcoming experience.