Did you read the post I linked to show how P2(W)PKH can be "exploited" too? Seems not. Again: A fad based on P2PKH tokens would be much more disastrous for BTC than one based on OP_RETURN tokens.

This is interesting and I have thought also about a related idea, but can it be proven that a private key exists for a given public key?

My related idea was a kind of "invitation-only" coin: that you have to derive a key always from another key and announce this derivation with a mathematic proof before you can transact value to them (i.e. create a challenge based on that PK). This would allow that only "spendable" keys could be created. But first, I'm unsure about the math, and second, that would not be really an "open", "free" cryptocurrency.

Perhaps also a proof that a public key is spendable is possible without deriving the key from an existing one?

However I believe even that can be used for data storage, but it would already make it more difficult (not necessarily more expensive though).

I'd have no problem if this particular problem is "fixed". However, the bigger inscriptions were only a problem for a short time in early 2023. Since then the focus has shifted to BRC-20, which is also the topic of this thread by the way, and BRC-20s were "compliant" to script size rules established before. In other words, for tokens like BRC-20, the "lifting" of the size limit in Taproot is irrelevant. This was also extensively discussed here. 

Now we have Runes, which are also compliant, but have cluttered a couple of blocks. I said already that I don't like their economic model. But I'm relatively "happy" that they exist and have driven BRC-20 out of the market, because they should take 30-40% less space if we consider how inefficient BRC-20 was. I think we'll soon see "blue" (<10 sat/vbyte) fee rates again.