Personally I've done work like this for agencies who focused on design and front-end that needed some complicated back-end functionality implemented for a client and didn't want to hire their own person internally to handle it.

This would really depend on the sort of agency and the type of work they're comfortable doing. Many agencies specialise more in "strategic" work, and have in-house resources for that, but when it comes to actual digital "production" work, this is something they might well farm out to contractors.

I focus mostly on front-end work with the ability to work on iOS, PHP, Rails and Phoenix projects. A lot of the places I work at get a lot of front-end work in and need an extra developer for a month or two then they like me and keep me around for a bit longer.

You'd be surprised. Many agencies don't have any web developers in-house, or have mostly front-end people and are understaffed for significant application-like work.