There are some off-the-shelf products that work similarly in the audio space:
I had plans to build something that for the TV, but having kids means I never had the time. And honestly, that might not have been such a bad thing since it made setting limits easier. I was able to teach my kid to turn the TV off when she was fairly young (and pause more recently), which seems to be enough.
I -have- built something like this for the TV using NFC cards, which was a great first-electronics-project for myself. That said, the most frustrating part is not the actual hardware itself but getting whatever streamer you're using to play the content you want. For example, this project required the author to WireShark and reverse engineer how Chromecast managed things.
If you do go down this route, I found that Plex offered the best deep-linking functionality and would wrap all of your content with that... but it was still somewhat unreliable.
These are also easy to DIY with a raspberry pi, rfid card reader, some blank cards, and phoniebox [0] for the software. I don't have much electronics experience and had it up and running fairly easily for under $40.
My daughter has a yoto and it has been absolutely invaluable for self directed learning and entertainment (with boundaries). But idk floppy disk seems way cooler to me!
Anyone remember the Sega Pico? These remind me of that. Such an awesome product!
We have a yoto for our son, and its a great experience, but be prepared for pricing of content to match what we used to page for cds/tapes. e.g., the pout-pout fish card is $8 USD for 10 minutes of content [1].
I think that's ok, as he actually would get a lot more than 10 minutes of use out of it, and its great to pay the creators while not having to worry about ads manipulating my kid. But it highlights how expectations for the pricing of audio/video content has changed (probably for the worse)... for me at least.
1. https://us.yotoplay.com/products/the-pout-pout-fish