I can’t speak to the research, as I have not reviewed it. But I can opine on the saichel of giving homework. A big tachlis is that it unites the school and home environments. The parents and hanhala doing the teaching need to be partners in raising the child. Each has important roles, and the more successful the partnership is, the better the product.
My opinion is that the material taught is only a vehicle to transmit the values of Torah and mitzvos. The ability to “spit back” the material that was ingested is reflective of memory skills, which is only one of many skills needed to grow into an adult ben Torah and Yirai Shomayim. The seforim on the mitzvah of Talmud Torah do extol the virtues of yediyas haTorah, but it is secondary to Ahavas haTorah. The latter promotes devaikus, the former is apt to be limited to downloaded data unless it is paired with Ahavas haTorah.