Why go for Magic Initiate?
- Versatility
Two cantrips to be used at will and a 1st level spell once for long rest can solve many problems in specific builds, or help characters do what they already do even better (ex. Fighter with Hex). Many times, simple spells like these can also unburden the main caster(s) of the group, allowing them to be more focused.
- Self-sufficiency
In groups/campaigns where magic is scarce, cantrips and 1st level spells make up for "holes" in the group. If your character usually scouts ahead of the group or does solo assignments, this is doubly true. Communication, illumination, reach... you choose.
- Flavor
Let's face it, to some people spell-less classes just feel... plain. Wouldn't it be great if 'Malakai, the Fighter' could be 'Malakai, Defender of the Enduring Flame', with Control Flames, Fire Bolt and Burning Hands? What about 'Nalia, the Monk" becoming "Nalia, the Feyblessed" with Druidcraft, Shillelagh and Faerie Fire? These are not the optimal choices, sure, but who cares - these guys are now cool!
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When is Magic Initiate a good option?
- If you're a Variant Human and/or have a feat to spare;
- If you're not MAD (relying on too many attributes to be decent);
- If you want a little more versatility and fun from a spell-less class;
- If you want a specific spell or cantrip from another class without multiclassing;
- For specific builds who need a spell for their 'combos';
That's about it, I think.