It's unlikely to happen because of how much of the work is contextual and that it's generally a constant demand.

Most gig work is context-free and on-demand. Pick up person at X spot and take them to Y spot. Pick up food from X and take to Y. You don't need to understand why, or how this fits into the rest of the person's evening/week/month.

Wages might go down, but I'd be surprised if something like Upwork overturned the software development market.