I would love to read this research if it existed in the public domain. However, much of this comes down to trade secrets and business practices. It's also not very amenable to controlled studies.
Practically speaking, these companies have a lot at stake in their hiring process. It's strange that so many people are convinced that the Big N companies are shooting themselves in the foot or otherwise making poor decisions with these interview processes.
Leetcode-style interviews might not have supporting research in the public domain, but absence of evidence is not evidence of absence. That is, just because the research doesn't exist doesn't mean that the Leetcode interviews are bad or worse than the alternatives.
Even if companies did eliminate Leetcode-style interviews, they have to replace it with some other alternative. Most of these criticisms fail to suggest actual replacement interview processes.