The wiki page you link to suggests "... quasi-public goods because excludability is possible", which in my opinion fits the bill for both read and write access to blockchains. They can, in the same was as roads, be blocked to poor overall usage.

But you are absolutely wrong about rivalrousness. A server providing readable data is infinitely renewable. It cannot be used up because the information is not deleted after being provided. You are confusing this property with excludability. It is a question of quality of service (which falls under the excludability property).

In this case, I would correct my definition to suggest that public APIs and public Blockchains, like roads and public libraries, are both quasi-public goods. Could we agree on that?