There isn't a firehose of new text being created in Latin, and you never (or very rarely) scan over something to find out what it's about, extract a quick fact from it, or decide if it's worth reading. You know what's in it, you know the standard take-away from it, there's a good chance you've read the highlights in translation already, you may even know one or two hair-splitting academic controversies about it, and you are sitting down for a good hour or several hours with it. It's a completely different kind of reading from scanning a web site or a newspaper to find something worth reading more closely, looking for the answer to a concrete question, or scanning something to decide if you can afford to not really read it.
The best analogy I can give is this: imagine taking Spanish from grades 7-12, culminating in a full year reading and understanding selections of Don Quixote. The entire curriculum builds towards this capstone year, and other areas of inquiry get very short shrift. Nobody cares if you can live comfortably in a Spanish-speaking country or watch Spanish-language TV. Nobody cares about modern idiom, or any more recent works of literature, or technical writing. s/Don Quixote/Aeneid + a small corpus of Roman poems/g and you have the bulk of my Latin education.
This sounds negative - we weren’t fluent in Latin! But for a teenager, it was a wonderfully deep exploration of Rome’s greatest hits. I loved it.
Humans naturally learn languages when they are immersed in the language. It sounds like Latin instruction was more focused on rules, and didn't provide that immersion before Foster. I can attest that many other foreign language classes also don't provide enough immersion to really learn the language, although being limited to ~10 hours a week makes that virtually impossible.
I can read German moderately well (can get through newspaper articles pretty easily, and novels with some effort), but I have very little ability to synthesize it (it'd take me quite a lot of effort to construct a sentence in writing, and I can't really speak at all). But the lack of ability to produce the language doesn't seem to negatively impact my reading ability.
... in the first few years of life. Beyond that, it's an intentional, conscious and often challenging effort for many.
Some people, even as adults, are far more adept at learning new languages than others. For the rest of us, it typically requires devotion to the subject for years.