It's definitely out there. Since you mention competing against Russian teenagers for $5/hour jobs, recognize that the gig economy/Guru.com/fiverr/etc. and real remote work are two very different things. If you want to have reliable work, you won't find it on the gig sites. You'll find it either by responding to a job posting, or through your network.
I'm a contractor, and many of the contracts I take on are long term and 100% remote. To date, all of the work has come to me in one way or another through contacts I have made in previous employment, friends, or people I have encountered in work on open course projects. That's why, to me, getting the word out to your network (and being remembered as a great coworker) is critical, since it will likely take some time to prime the pump if any work is going to come. When I first started looking for contact/remote work, I was putting it out on Facebook, on LinkedIn, to my friends, etc. regularly for about six months before I find my first contract. Since then, it has gotten a lot easier. I make it a habit to tell everyone I work with what a pleasure it has been to work with them, and to please keep me in mind for future work.
Sorry if that's more of a digression into contracting than remote work, but there's some crossover.