This is an example where it plays a role. In Slavic languages, you would say something like “I saw that good one” (inserting a definitive article substitute) or “the one I saw was good”; in English, you don’t need the latter phrasing with “a”; indeed, it is somewhat artificial example.
What the parent post was saying was well described by his examples of where the article is obviously superfluous and doesn’t provide contextual information - which is the majority of their uses. There are situations where articles carry information (nobody disputes that I think), but they are used far more frequently as grammatical filler.
“I saw that good one” -- translated to Croatian, this wording strongly implies that both knew upfront which movie was good and he watched only that one. But according to the parent's explanation it may not be the case, Alice has only learned that one of the movies was good.
and
"The one I saw was good" (he picked a random movie from the collection and it happened to be good -- which would be "a good one" from the parent's example).
What the parent post was saying was well described by his examples of where the article is obviously superfluous and doesn’t provide contextual information - which is the majority of their uses. There are situations where articles carry information (nobody disputes that I think), but they are used far more frequently as grammatical filler.