The sentiment tells me that they do not understand child development, or have been misled.
One of the main critiques I hear from adults (when I tell them that I pulled my kid out of public school and now he has child-driven, play-based learning) is a derision of play. They think of play as extracurricular- only to be rewarded to kids when the "real work" is done. And certainly, that is how public schools treat free time these days. But it's flat-out wrong. Not only do children learn best when playing, but they need full body and mind immersion to really understand a topic. Sitting quietly in neat rows putting pencil to paper is not the best way to educate. It is the method that has won out in public and private schools- but not because it is superior in terms of education and retention. It is superior in one way alone: to ensure control over so many children. If control is what you are after (and as a former public school teacher, I can tell you- it is exactly what they are after- only they call it "classroom management"), then enforcing rules and blind obedience, insisting upon silence, and forcing children to ask for permission (to meet their bodies needs to move, stretch, take a mental break, eat, and urinate) is exactly what you do.
While this is OK (never superior, though) for many kids, many "square pegs" who don't fit the round holes of standardized education get ostracized, apathologized, and judged as inferior using this method. I overheard kids who fidget being called "problems" and "distractions" in my kid's school, and I saw kids with physical or behavioral outbursts having their recess taken away (when in reality, the outbursts would likely subside if they got MORE recess). This method of academics through behavior management is superior only for a certain type of kid- and the others (atypical neurology, highly creative and imaginative, gifted and needing more, children needing more one-on-one time to help them comprehend, or highly emotional and empathetic children) get shut out and left to fend for themselves (or their families have to pick up the slack outside of school hours). All juvenile animals learn by playing. They mimic adults, take things apart and construct them, go on discovery walks, and create rules and negotiate with others. The academics follow, I promise you. When child is motivated by a topic (say, learning to cook a meal), they read the recipe, follow instructions, measure things out and learn about chemistry- all in one activity. When adults are there to guide, offer isights, question them about their process and the whys, and answer questions, the learning is focused, documented, and clarified. When my child was driven to play an adult game (Dungeons and Dragons) in 1st grade with his parents, he was motivated to learn to read. We told him, "This game requires a lot of reading and memorization of rules. So you need to be a better reader, then you can play." Now he is an avid reader, well ahead of "grade level" and reads daily on his own (thanks RPGs!). We read to him every night before bed, listen to audio books in the car, played phonics games with him, and he was reading books before he entered school. His reading level has gotten more advanced because he loves stories, imagination, and wants to be functioning in the world with others. He loves new words and any time he hears one, he has the confidence to stop the conversation and ask its meaning. I hear him using the word himself in the days following. This is the epitome of a child-driven learning and it has taught my child more mathematical concepts and a love of learning than any classroom teacher has. When my child decided his passion was marine biology, we learned all we could about the ocean and its creatures- and dang if he didn't make our trivia team win one night because he learned so much on his own! If you still doubt the importance of play in education, I suggest reading books by John Holt. They may change your mind!