One of the biggest perceived benefits was that it skipped over a lot of the rote memorization, drilling, and "grind" work that young students often struggled with — it let them engage quickly with the actual stories and texts that could make reading meaningful and fun.
Reading Recovery blew up, spreading to the UK and the US. It was super influential in the 80s, and many of its proponents argued that phonics was fundamentally flawed in comparison. A relic.