Having been on the other side for quite a long time, I can assure you that despite best efforts by some very well meaning and smart people, this is the only process that has stuck around (and is still growing). That's because it's the most convenient method to interview at scale.
When a company is very small and/or only hiring one or two engineers a quarter, choice of interviewing method doesn't really matter a whole lot. You will have enough time to interview people and any method you follow will give you a decent candidate.
But when you are a coveted company with a strong candidate pipeline and are tasked with hiring 25 engineers a quarter (which was the case with the leadership team I was a part of), or thousand at Google scale, you need a process that is fast, efficient and convenient. You don't necessarily need a process that's best for candidates; as long as the process filters in enough candidates, and doesn't waste much of your team's time, you're good.
There are some other reasons this process has stuck around, but that's one main reason. I don't see it going away any time soon.