Answer: I think a lot of people have probably wondered the same thing. But part of the answer is that "scales" don't really precede "melody." We are very used to thinking that we are now going to write a melody in major, or in minor, or Dorian, etc. and forget that really we just should just think of the melody. "Scale" or "mode" are terms that can be used afterward to describe the pitches that ended up forming the melody.

And as you say, their order is not going to be just ascending or descending. So to say that a melody is "minor" or "major" or "Phrygian" or "Dorian" means that it has certain characteristics associated with that scale or more.

For example, a major melody will emphasize the major third above the tonic and will also use a leading tone below the tonic (i.e. a note one half-step below the tonic). Those are two important characteristics of a major melody; the other notes of the major scale don't need to be there and we still feel that "major" is a good description. "Minor" will of course emphasize the minor third above the tonic, and we can use further descriptive terms depending on what else happens. Is the 7th degree frequently raised? You could call that "Harmonic minor." Are there places where the 6th degree gets raised too when ascending to a raised 7th? That's called "Melodic Minor," but the same tune may have a low 6th and 7th in descending passages. If a melody that is otherwise "minor" tends to use a raised 6th degree the term "Dorian" will apply, even if other notes of the Dorian mode are not present. A mostly minor melody that frequently uses a minor second above the tonic may be called Phrygian, just because that minor second is the main defining characteristic of the Phrygian mode.

Melodies can mix modes, with one part seeming minor and another part major, etc. So the main thing to remember is that the terms "scale" and "mode" are useful in describing the nature of certain melodies, but that doesn't mean those melodies necessarily stick to the notes of a particular scale or mode. So: don't worry about maintaining the nature of a particular mode (unless this is a school assignment). Just know what it is that is most important about each. These are not full descriptions, just the highlights of each scale or mode:

Major: major third above tonic, leading tone below tonic
Natural Minor: minor third above tonic, no leading tone
Harmonic Minor: using a leading tone in minor
Melodic Minor: sometimes raising a sixth when rising to a raised seventh (leading tone).
Dorian: natural minor but with a major sixth
Phrygian: natural minor but with a lowered second
Lydian: major but with a raised fourth
Mixolydian: Major but with the 7th lowered to avoid a leading tone.