I suppose one could come up with a dramatically new approach and "market it" to get a lot applicants. But I think the current process, while deeply flawed, probably does at least correlate with good engineers, and such a process would perhaps be biased towards poorer applicants. At the very least, I can see how there's the expectation of that, and that alone is enough to prevent it from happening.
The problem is I'm sure we've all worked with people who had impressive resumes but were unproductive and probably couldn't pass FizzBuzz, and we all want to avoid that. I would imagine that making the labor market a little more fluid would help, so companies bias more towards hiring without a bunch of arbitrary tests, and are more inclined to let a poor performer go early. But it's still hard to really see someone's potential for several months, because it can always be blamed on getting up to speed, onboarding processes, etc. There are companies who don't hesitate to let poor performers go (e.g. PIPs and up-or-out positions), but companies that do that a lot are widely regarded as having toxic, corrupted versions of such a process. I wouldn't actually bet on it being a net improvement.