The big-cos are also leaving a lot of talent on the table -- which makes it silly when they talk about a "talent-shortage." But, they're also paying enough where people WILL game these interviews in order to get the job... So the best argument I've seen for why these interviews work is that it selects people who work hard at learning this type of problem solving, to get the job... which correlates well with how hard they will work at the job.
Having an "objective" process is near impossible... and in fact probably not something one should strive for. Everything we do has humans has intuition behind it, whether good or bad. I think intuition is very important for finding a maximal team, especially a small one.
"Inclusivity" is kind of weird here.. most often you'll want someone with domain knowledge to get a project going quickly.. It's definitely less important for big-cos, but you still end up interviewing for a web job, an iOS job, etc.. so domain knoweledge does come into play.. at least at the big companies I've interviewed for (google, fb, lyft, uber, etc..)
I doubt this process is risk averse... you'll find people smart enough, but you learn little about their character.
Relevancy seems like a joke in your list... unless all you need is people to iterate on a small set of already solved algorithms in slightly different ways. I'd say that applies to zero companies. Except maybe leetcode, which helps people study for these tests.
The process scales well, and is easy to do, i think thats its strong suit... it's mostly effective across a ton of people.
So in summary, I agree that it seems like the best known process for these big companies. but I doubt it's as risk-averse as you think, and if you truly have a talent shortage, it's an artificial shortage created by your interview process. You might need to take some risks on people if you need to grow faster...
That being said, having that big-co process is great for startups! There's a lot of exceptional talent out there that will fail at the big-cos interviews, but will be better than their engineers for your team :) (There's also exceptional talent that will succeed at those interviews too, but would rather work at a startup) It might be a matter of using your intuition to find them... it's definitely a hard game.
I think this recent data-driven trend that is spreading across all realms of companies is poisonous in some areas where it does not belong... Human intuition still wins in a lot of areas, if it's good.