I don't think so personally. I think the internet is so vast, that anyone can set up shop on the internet and get paid. There will always be people competing with you, trying to do better than you. And with so many people working online, it means it'll be tougher for some of us to find work. But, I think the ones already established and working online for years will be just fine.
I think though, that eventually gig sites and other freelance sites, will be over-crowded by the same style of gigs, with very little differences. It's why I focus on making my own sites instead of working on gig sites.