Random company blogs and random UK news blogs aren't the authorities on what a backdoor is.
You look at something like, for example, Wikipedia, and it basically agrees with my take above: backdoors are usually covert, but are intrinsically somewhat fuzzy to define. This is how the word is typically used in common conversation.
> This would not be wanted by the end-user. The backdoor in this case is just an imposition on the receiving party, i.e. the merchant, that they'd rather do without.
Speak for yourself, this is literally the selling point of GNU Taler, this is one of the reasons people are interested in it. They put "taxable" in the tagline not just out of an interest in transparency but because it's their main "hook" to get people interested in the system.
Once again, I talked about this above, but backdoors are a fuzzy concept where different communities can end up with different conclusions about what does or doesn't fall into the category of a backdoor. The fact that you personally don't want income levels for merchants to be auditable by the state does not mean no one else wants that transparency (merchants included).
Once again, taking that idea to its logical conclusion would be absurd. A nontrivial number of software merchants would like it if my browser didn't have inspector tools and didn't let me look at the source code of pages that they sent me. A lot of web publishers would like it if browsers didn't have tools that let people intercept and modify HTML before it gets rendered to the page. That doesn't mean my browser inspector or my adblocker is a backdoor. These terms are in part socially defined, and yes, expectation and transparency are a part of how we do that. They're not the only part, but they are a part.
You posit a world where any disclosure of any information where anyone would prefer that information to be private is a backdoor, and that broadens the definition of a backdoor beyond the point of usefulness and beyond the scope of how most people and most articles online use the term.