Fair point. The companies are small and medium-sized. I'm not convinced that those models can't scale, though. One large-ish company that I know of who still does something similar is ThoughtWorks. They have on the order of thousands of employees and their interview process consists of, among other things, a take-home code submission and on-site pair programming.
If you're getting 1000 resumes per day, I think you would be able to weed out a significant number of them just by giving them a coding assignment to work on. Churning out a resume is easy, but sitting down for a few hours and writing well-designed code takes effort.
They probably can scale up to a point. Thoughtworks has 2100 employees. Google has 45,000.
How would you grade/score ~1000 code submissions per day, though? You could conceivably do Coursera/Topcoder-type automated grading, but that can only get you so far and can't distinguish good code vs. bad code vs. "copied from Glassdoor" code. It might be useful as an initial filter, though. You'd have to constantly be implementing new questions w/ associated grading scripts, though, as the problems would inevitably leak.
If you're getting 1000 resumes per day, I think you would be able to weed out a significant number of them just by giving them a coding assignment to work on. Churning out a resume is easy, but sitting down for a few hours and writing well-designed code takes effort.