Pick up a neuroscience book and you're going to quickly find out why your statement isn't possible. Have you ever had to conduct tech interviews or spoken to people who have? Tech interviews are the biggest crapshoot you'll ever see, for every 100 interviews you'll be lucky to find a single person who can code fizz buzz on the fly, introduce a small variation in fizz buzz that requires them to be able to read their own code and they can't modify their own code. The number of people who have a long enough short term memory and can concentrate on a single thing for three hours straight is exceedingly small.
Even the very best tech companies are constantly filtering through thousands of people who claim to have worked on extremely complicated development projects but can't code extremely simple things.
Yeah larger desirable companies already have no shortage of well performing candidates to choose from so why make the interview more fair in any way? That would just make selection more difficult for them. Smaller companies might not have this issue but will probably follow the practices of larger, more successful companies anyway.
Why would this be the case--at places where the number of candidates far exceed positions? This is the exception rather than the common case.