Write down the definition of a token. Write down the definition of a stock. If you look at them carefully you'll at least see a lot of overlap. For bonus points, write down not the actual definition of a token but the definition of a token its advocates want you to use; it is particularly this one that in my opinion is already what a share of stock is.
I can say you need to be careful. It sounds like you've written in to the definition of a "token" that it is "meaningless", and that is a philosophical overreach, not an accurate statement. As the reply chain correctly tried to point out, nothing stops the same process that turns your abstract, "meaningless" number that represents your shares of stock into a meaningful number from being applied to a block chain token. Our entire economy is made from top to bottom out of "meaningless" things given meaning by convention, law, and other forces. Getting too reductionistic leaves you confused about not just tokens but a lot of things.
And on the flip side, if you actually dig in to what a "share of stock" that "you" "own" is, it is already not "some fractional ownership that carries legal rights and a claim on assets" and is already more complicated, abstract, and partial than you think. Just as the token advocates want you to think of a token as something more than it is, the stock system is not in a hurry for you to understand what it is you actually hold, but it certainly is not simply some fractional ownership in the simple way you probably have in mind, and there are more exceptions and caveats and legal ways you don't really own it as much as you think already in the system. It's already more a mere "token", in the sense you originally meant, then you realize.
Again, that's not true. As a matter of law, a bank balance is a debt the bank owes to you. An NFT or a bitcoin is a row in a spreadsheet that records the exchange of notional nothings.
A BTC is not notional nothing. What determines the value of a thing? The market does. Not you. The market. And the market has determined that BTC has value, and that's been true now for 16 years and counting.
At any rate, to the tokenized stock example, if you are purchasing a tokenized stock represented by a company such as Robinhood, it too is a debt in that the token is exchangeable for the underlying.
This is an even higher level of guarantee than, say, an options contract, in that the reserves are provable. It does, of course, involve trust in the intermediary, just as your bank balance does. But at any rate, this financial technology is an expansion of what isolated databases provide to the market.
There's no conflict: Markets can remain irrational for a long time and they can certainly place a high value on notional nothing. This piece of cardboard is worth $500,000 https://www.pokevalues.com/card/illustrator-pikachu-japanese... but at least that is rare and has a cute pokemon on it.
If a company chooses to list its stock on a blockchain instead of the NASDAQ, then, sure that could have the same value as a traditional stock assuming it confers the same rights.
Crypto tokens are just some meaningless entries on a blockchain.