Can tags replace a physical album for children?
They can give a child a physical object that starts a story, which is most of what a record sleeve ever did. What a plain tag cannot do is work on its own, because something has to read it, and that something is an adult's phone unless you buy a device built for the purpose.
What the appeal actually is
A child who can choose what to listen to by picking something up is doing what people did with records, and the value is in the choosing rather than in the audio.
It is also a way of putting a limit on the choice. Eight objects on a shelf is eight options, which is a different experience from a catalogue with no end.
Both of those are real and neither requires NFC. NFC is simply the cheapest way to attach an address to an object a small child can handle.
Something has to read it
A tag is inert. A card with a story on it does nothing until a reader is brought to it, and in a home that reader is a phone.
So the honest description of the phone version is: the child chooses the object and an adult taps it. That is still worth building, and it is not the independence people picture.
Take NFC Tools. On iOS it requires an iPhone 7 or later running iOS 15.6 or later, and the app must be launched manually. Background reading is available from the iPhone XS and XR onwards.
Understand this before buying a pack of cards to write on, because it is the point at which most home built versions are abandoned.
Purpose built players
Devices exist whose whole purpose is to read a figure or a card placed on top and play the audio associated with it, with no phone involved.
These solve the independence problem properly, and they solve it by being a closed system: the objects are theirs, the catalogue is theirs, and a tag you write yourself is generally not accepted.
That trade is the decision. A closed device that a child can use alone, or an open pile of tags that needs an adult.
Building the phone version
Use cards or wooden discs rather than stickers, since the object is the point and a child will handle it hard.
Print the picture large and the words small. The child is identifying it by the picture and cannot read the address anyway.
Point each tag at an address you control, because a set of thirty story cards is exactly the kind of project that outlives the service you first used.
And write them unlocked. What a four year old wants to hear changes, and so should the cards.
Frequently asked questions
Can a child use this without an adult?
Not with a plain tag and a phone. Something has to read the tag, and a phone is not a device you leave with a small child.
What about the players made for this?
They solve it properly by being closed systems. The objects and the catalogue are theirs, and your own tags are generally not accepted.
What should the cards be made of?
Cards or wooden discs rather than stickers. The object is the point and it will be handled hard.
Will the set still work in five years?
Only if the addresses do. Point them at a domain you control so a service change is one edit rather than thirty.