I'm not going to personally install this and I'd pay publishers for their content. What I won't do is sign up for an expensive yearly subscription that is generally made difficult to cancel just so I can read a handful of articles a year.
Newspapers really need to offer a payment option that allows me to purchase access to a given amount of individual articles or purchase access to the entire site for a given published date just as if I'd paid for a printed copy and that access needs to be permanent.
You expose valid concerns and go beyond proposing possible solutions.
There is probably a more complicated issue here, about difference between media agencies, and authors as content creators.
At least, what you do is the positive and creative way to approach the problem. Probably a browser extension is not going to ruin the industry but
is perpetuating that wrong mindset about how everything in internet must be free. A publishing model close to the vision you refer is the magazine subscription. Once we talk about the newspapers model, solutions turn into a challenge.
Newspapers really need to offer a payment option that allows me to purchase access to a given amount of individual articles or purchase access to the entire site for a given published date just as if I'd paid for a printed copy and that access needs to be permanent.