The quick and insufficient answer is, "Yeah sure, most scales are the same forwards and backwards. If you're looking at a page that lists, like, 'C major ascending, C major descending,' etc., then it's just because the melodic minor will be different descending, and they're trying to be overly systematic."
But at its core this is a question about semantics. We use the word "scale" in multiple ways, and you've noted one of those uses, when there are others that can make more sense of this.
The way you're using "scale"—"a grab-bag of pitch-classes from which we select notes to assemble to form a melody"—well, yes, the word is sometimes used in this way. Often in jazz circles, e.g. "Don't play that C sharp; the chord here is a Dm7, so solo in a D dorian scale," meaning not that one simply runs up and down the dorian scale sequentially, but that one selects from those pitches. If we want the most technical word for this concept, maybe "pitch set" is best.
Some comments here have also mentioned "mode." Or, colloquially, we often talk about the same idea with the word "key." Superficially, this seems like the concept you're referring to: The mode of C major is all naturals; the mode of D mixolydian has an F sharp; etc. But this word can bring in an additional meaning: "mode" and "key" are, in most contexts, bound to the notion of "tonality." That is, if we're in C major, we don't just use all the naturals at random; to do so would be atonality. Rather, we have a sort of grammar or syntax in which pitches (and the chords underlying them) have purpose, and order themselves according to those purposes: I leads to V leads to I.
To come back to "scale": This idea of syntax can also be bound up in the word "scale." We're looking at you, melodic minor (we have been all along, haven't we?). It has different notes going up and going down—not because somebody made up the "rules for the scale" first and then composed using them, but because practice did it first. The fact is, for the bulk of the "Common Practice Period"—that roughly baroque-through-romantic monolith of "classical music"—scales are an actual building material. Make a survey from Vivaldi to Rachmaninov and it's a trivial exercise to find entire, intact scales scattered throughout concert pieces, as if lifted straight from Hanon or Flesch. And even easier to find them in fragments, as scalar motion. Think through the theme of Beethoven's "Ode to Joy"—a couple of thirds, one big leap, and otherwise everything is stepwise. And as the underlying chords, the gravitational forces of tonal harmony, exert themselves on these scalar melodies, this is where the cadential tug in melodic minor, as it demands a "proper," major, dominant, warps those 6th and 7th scale degrees upward, while the falling motion, perhaps supported by something like a dim ii, lets them relax.
On re-reading this answer, the mention of Hanon and Flesch reminded me of another very good reason for finding descending as well as ascending scales. If the conversation is simply about music theory, then yes most garden-variety scales are symmetrical. But if we're talking about actually playing them on an instrument, there are practical considerations. The fingering may be different on the way down for many instruments, and even if it's symmetrical, the task of using the same fingers in the opposite order is one that must be learned.
