Two reasons. First, the concept of the feat is that you are dabbling in the basics of a class's spellcasting system, so the mechanics would naturally follow that. Second, feats are supposed to work for anyone who takes them, granting an ability if you don't have it, or augmenting it if you do. Treating the once per day casting as a spell slot does this.
The likely reason for how the feat is written is that it ignores the differences in spellcasting systems. Yes, it was written this way deliberately, but I don't think it accomplishes the intent behind the feat.
Granting a spell slot messes with the established way to blend multiple casting sources(i.e. multiclassing).
If a barbarian takes Magic Initiate, it's effectively a single spell slot, but it's not really useful as such because the Barbarian only has the one "slot". In this case, formally calling it a "slot" is pedantic. I really don't care because it has absolutely no impact on game play. If someone has a use case that disputes this -- without multi-classing -- I'm all ears.
Once you're dealing with a character that already has spell slots, it's a different story. Once you've got spells from two different classes, you ignore either class's specific slots and use the multi-classing table. You have two ways to rule on the Magic Initiate feat:
1) Per Crawford's statement that the feat is
not intended to let you throw the gained spell into your general mix of slots. In this case, it's a completely separate ability and exists in a silo. The Wizard can't gain
cure wounds this way and use one of his 3rd level slots to cast it. Nor can he use his 1st level slots to cast it multiple times in a day. Logic would indicate that the inverse is also true; the Wizard can't forego his use of
cure wounds to eek out another
magic missile. In this case, the spell has its own, completely separate, refresh mechanic. Based on that, it doesn't sound like a "slot", per say. I sure wouldn't let a Paladin take the Magic Initiate feat to gain an extra smite.
2) Ignore Crawford and treat the feat as though it actually represents some minor foray into one of the established ways of casting magic (i.e. mini-dipping into a class). In this case, use the established multi-classing rules. The above Wizard can still freely mingle his normal spells with
cure wounds. Also, the Paladin who casts
magic missile does so at the cost of a potential Smite. All other class slot progressions are ignored in favor of the multi-class progression. IMO, this is the most natural and logical interpretation of the rules. IME, it is also completely balanced and fair.
One note on option #2: If you're a single-classed caster that uses this feat to dip into another class, the progression is the same for full or half casters whether you look at your class or the multi-class table. For 1/3 casters (Eldritch Knight and Arcane Trickster), the progression is a bit wonky. Use the single-class progression. The feat is a mini-dip. Use the existing rules as a framework, not a straight jacket. If that doesn't make sense, then Crawford's advice is probably best for your group. You should also buy scissors with rounded tips.