It's important to understand that mode doesn't have to be, and often isn't, an explicit choice. You wrote:
The notes we play and the order is based on sound and emotion.
and that's true enough, but—if you've mostly written notes from a single western key and are writing in a more or less traditional style—then the way you've used those notes will be in a mode whether you intended it or not. One of the notes will almost certainly be the primary resting note, that's the tonic of the mode. You will generally lead to that note from a note that is a half- or whole-step above or below. Approaching from the half step below implies that you're probably in Ionian or Lydian. Half-step above implies Phrygian or Locrian. Etc.
Every mode has unique relationships between the scale degrees. Only one mode has a lowered second scale degree and a diminished fifth scale degree above the tonic. Only one mode has a half-step below the fifth and first scale degrees. It's silly to say that any particular relationship is "happy" or "sad", because both music and human emotions are more complex and variegated than that, but a composer will generally learn that certain modes work better for some kinds of pieces. They'll have favorites and least favorites, ones that are comfortable, ones they find challenging—and thus they sometimes will start by deciding what mode to use before writing—but generally the music will be in a mode regardless.
Of course, it's worth noting that there's no law that says you have to use any modes. You can use all 12 notes equally, you can use microtones, you can compose using only 5 different pitches. Modes can be a convenient framing tool, and most western composers and song-writers tend to write using them, both on purpose and coincidentally, but plenty of us ignore them entirely.
EDIT TO ADD: I realize that I had left out another important aspect of modal composition. Due to the way composers tend to use a certain set of scale degrees as relatively stable (in most cases the 1st, 3rd and 5th scale degrees primarily), and the tendency for half-step melodic motion to have more urgency when leading to another tone, different modes have different "gravitational" direction and strength. Lydian has a marked tendency toward upward melodic moment, while Locrian tends to have a very strong pull downwards. Dorian, by contrast, tends to not feel a super strong pull in either direction. To be sure, no composer has to follow these tendencies, and we will exploit or not exploit them in whatever way that fits the material, but the gravity is there nevertheless.