The only interesting point they make to chew on is that holding a physical object might help people forge stronger bonds with an these artifacts. However, the people most likely to be impacted by this is small children - the same ones that put things in their mouths. Montessori schools are all about manipulatable objects, ideally made of natural materials like wood.
I dunno, this seems noble enough and I don't want to shit on such a clever project. I just fret that 3D printed objects are expensive, breakable, likely to be stolen (accidentally or otherwise) and well, I can't help but feel like all of this is going to end up on the same garbage ship to Liberia some day.
Please, bring me to the other side! I want to love this.
The positive thing about the 3d printed objects is that kids can choose and print them themselves. This has the benefits that the kids (a) get some hands-on 3d printing production experience, which is a fast gateway to wanting to make your own 3d models, which is a useful and empowering skill and (b) I have found that 3d printing a cultural artifact creates an incentive to learn more about it -- consumer 3d printers are so slow, it gives you plenty of time to ponder the item being printed, as well as the post-processing/finishing step, it builds an intimacy with the object you wouldn't have just walking by it in a museum. It might be hard to buy into this idea, but I have personally experienced it when printing scans of sculptures like the Pieta from the Vatican or Rodin's Thinker -- it motivated me to dig in and learn more about the background and nature of these works of art.
But yes, there is the issue that at the end of the day you are just pushing more plastic waste into the world. My adult daughter kind of hates my 3d printer for that reason, and I can identify with the angst. I wish there was a better story for PLA recycling.
I was a little surprised to find it is a closed EdTech commercial product and not open source. The whole thing feels more like a Hackaday project than a product offering. It is the kind of idea that when you look at it, you instantly get how it is built and can see how you could assemble one yourself given a week or so of time to tinker with a 3d printer, a Raspberry Pi, and another $10 to $20 of electronics, and make your own decisions over how much to focus on audio vs. putting a touchscreen on it as well. There just is not that much to it. And to have no real way of engaging other than as a big name museum they want to partner with, it is off-putting and discouraging -- this thing could have some real legs if it was open source. As it is now, it feels like they are artificially constraining the growth and application opportunities by holding the thing close to their vest. Good luck to them I guess, but it seems like a mismatch.
Yes, yes, "execution is everything" and ideas are a dime a dozen, and if it is so easy to build why haven't I made one yet? All good points.
I've heard this before. I've also read that its not that the items are rotated, but they never see the light of day. And its not just less significant works.
Michael O'Hare of UC Berkley argued that museums should sell or at least lease out much of their unseen inventory and use that money to lower or even eliminate admission fees. 
Certainly something better could be done. Museum in a Box is at least a step in the right direction
Part of the issue is the museum mafia puts onerous restrictions on the extent to which museums are allowed to sell off bits of their collections. That's why so many items are stowed away never to see the light of day. If they sell off items, they will be blacklisted from ever receiving a touring/visiting collection, which is the big money maker for additional admissions fees and bringing folks in who have already seen everything normally on display.
The code of ethics of the American Association of Museums explicitly forbids selling items from collections to meet operating expenses, and they will ban museums from receiving loans of artwork if they do so.