The main reason to this isn't what Amethyst and Kiawe said, you almost answered your own question actually. The list of yours has some reasons because of why the Azurill line is part Fairy-type.
You listed "based on actual fairies" as a criteria for a Pokémon to be a Fairy-type, and that's the main reason because of why the evolution line is part Fairy-type. I'll elaborate about this here.
Have you ever heard of Naiads and Nereids? They're fantastical creatures in Greek mythology, and are flowing water (springs, rivers, fountains, lakes) or sea Nymphs, respectively. Nymphs (Greek: νύμφη) in Greek mythology is a large class of young female deities typically identified with natural, fertile and growing features such as mountains (oreads), trees and flowers (dryads), springs, rivers, and lakes (naiads) or the sea (nereids). We're interested in the latter two, though, so I'll talk about them.
Naiads were the nymphs of rivers, lakes, streams, marshes, fountains, springs, brooks and any other type flowing water. They were minor goddesses and appropriately in their relation to freshwater, were represented as beautiful, lighthearted, and beneficent. Like the other classes of nymphs, they were extremely long-lived, although not immortal, which is rare for even minor gods and goddesses. Usually, they lived above Erebus (the underworld) and Tartarus (the deep abyss which was used as a dungeon of torment and suffering for the wicked and as the prison for the Titans), but the five rivers of Erebus also had Naiads, for example Minthe, the daughter of the River Cocytus, who had a really bad ending because of her affair with Hades. Usually they were lighthearted and, above Erebus, they were amiable companions of the major gods and had a nice rep with them (you might be able to associate Marill/Azumarill with them if you look closely).
Nereids were a bit more beautiful and "specific". They were fifty sea spirits, and they were known throughout the world for their beauty. They had long flowing hair, as dark as midnight, sea-green or blue eyes and gossamer white and blue dress which billowed around them in the water. They were daughters of the former ruler of the seas, Nereus, who was the son of Mother Earth and the Oceans itself, Gaia and Pontus. They (Nereids) were known to help sailors on their voyages when they faced fierce storms (also see: Azumarill's Alpha Sapphire PokéDex entry. Note the similarity.). The primary role of the Nereids though was to act as attendants to Poseidon, and so they were commonly seen in the company of the god. Whilst associated with the Mediterranean, they were thought to be specifically concentrated with the Aegean Sea, for this was where their father, Nereus, had his palace.
Now that I've explained the two, how are they related to actual fairies, though? Nymphs were the fairies in Greek mythology. A fairy is a small imaginary being of human form that has magical powers, especially a female one. Nymphs fit this explanation totally, and in the Iliad, Homer describes Nymphs as "a natural female magical deity", thus cementing the fact that they're Greek fairies.
Now, how're they related to the Azurill line? The said line is considered to be closely related to fairies (not magical, but design-wise and characteristically), as they're in the Fairy egg group also, and they do look like fairies. And they're part Water-type, too, so water nymphs and the line (except Azurill) are pretty related to each other, characteristically. If we look at other Water-/Fairy-types, Primarina and Tapu Fini, they're also like nymphs if we look at their PokéDex descriptions (Tapu Fini's description might sound weird, but Nereids were like that, too, spreading destruction when angered).
Now, let's compare the line with your list:
- Pink ✓ (ears)
- Pastel ✓ (their palette is light)
- Humanoid ✓ (almost)
- Small ✓
- Feminine ✕
- Trickster ✕
- Magical ✕
- Based on actual fairies ✓
- Smells or tastes good ✕
- Cute ✓ (relative, but most will agree)
- Pretty ✕ (relative, I don't find them very pretty though)
- Healer ✓
- Linked to nature ✓
So, even with conservative estimates (which would strike some the ticks off), we're getting at least five points which fit the Azurill line, and with some leniency, we get eight.
Now we can have the points put forward by Amethyst and Kiawe.
They may have wanted to make it more competitively viable. Water/Fairy is arguably better than Water, and STAB Play Rough + Huge Power is brutal. They also may have thought they didn't retcon enough Pokemon to Fairy type, and they needed another.
commented 13 hours ago by Amethyst
True -- dual STAB options are usually better than single STAB, and the second reasoning doesn't strike me as concrete, but it might be true.
It's just GameFreak logic, if not balancing purposes. Azurill line's ears are pink, and you could say that Azurill is small and cute (though the latter is subjective). Azumarill also looks pretty humanoid, and not being "magical" is somewhat dumb. How can you faint Pokemon by just singing a song? (Perish Song) Moves like Light Screen, etc. are also not something humans can do. Its dex entry mentions that "Azumarill can make balloons out of air. It makes these air balloons if it spots a drowning Pokémon" which fits both healer and linked to nature criteria.
commented 12 hours ago by Kiawe
I disagree with the GameFreak Logic point, but yeah I agree with everything else.
Now that we're almost done with the answer, I'll provide a tl;dr with all the points discussed here.
- Related to Greek mythological sea fairies
- Fits a lot of criteria according to your table
- Competitive viability raised because of Water-/Fairy- dual typing
So that's all for the answer, let me know if I missed anything, hope it helped!