Not to mention the various added value innovations to make a particular blockchain attractive and useful to some people.
No, that's not really correct - and this is exactly what I'm talking about. Saying a blockchain is all of these things is like saying a website is the backend application, the client web browser, the TLS protocol and all the users who use the website. But most of those things aren't the website.
When we talk about the architecture of any given web application, we decompose these interactions and distinguish between them. We generally even distinguish between backend, frontend, infrastructure and and middleware resources on the server side. This allows us to productively talk about things with precision. In contrast any discussion involving the term "blockchain" suffers because it means 10 things to nine different people.
It's not even an issue of generality. It would probably be fine if the term "blockchain" referred to entire networks and protocols built over blockchain data structures. Then referring to a blockchain would be like referring to "the internet." The real problem is the lack of precision, because in conversation different people are crossing all sorts of layers of abstraction, each to varying degrees of knowledge and expertise. That makes ascertaining the accuracy of claims a murky business for those who aren't substantially well informed.