NYT will let you hit any number of pages; your paywall quota is only consumed by those where you are interested enough to click "Show Full Article."

I do not think this is the case. I tested this out by clicking on several articles without hitting "Show Full Article" on any of them. On the first article, I was told I was reading 2 of 10 free articles. After 8 clicks I hit my quota.

It's to expose you to the links underneath the article.

After reading the headline and first paragraph, many people would bounce (especially on mobile). By giving them alternative exit strategies, the button marginally increases traffic.

(Yes, this has been rigorously tested.)

It is to speed up page loads.

Most likely, the page is being rendered to HTML on the server and then client side javascript picks up where the server left off, once it has loaded and launched. So, you get the full page load, and >then< the javascript checks to see if it should display it.

The alternative is to have the page hide the content initially and have the javascript re-enable it, but this would involve a flash of 'closed page' for actual subscriber and people who came via google.

Companies want paywalled content to be indexed by Google.

I always assumed that was done as a metric, so they could see what percentage of people who saw the page actually read it. But admittedly that is just conjecture.

It doesn't do that on mine, benefits of blocking all their scripts I guess.

Try throwing in privacy badger, ghostery and no script, then see if it still does it.