I look at this in terms of how the classes were developed historically. Of course this is going to lead to the inclusion of certain D&Disms which, for D&D, I feel are quite appropriate!
1. The fighter is the full-capability armed combat class. Archetypes that excel at armed combat fall under this class and can be expressed as subclasses. The paladin subclass, for example, is a fully capable fighter with additional divine magical capabilities balanced by restrictions such as vows of charity, poverty, chastity, etc.
2. The magic-user/wizard replaces most of the fighter's armed combat capability with arcane magical capabilities and is minimally capable with armed combat.
The natural gestalt of the above two classes is the fighter/magic-user multiclass, best expressed in 5E by the Eldritch Knight archetype, and is moderately capable with regards to armed combat which capability is then supplemented by magic.
3. The cleric is an alternative to the fighter/magic-user, replacing the fighter/magic-user's arcane magic with divine magic. The druid subclass re-flavors the cleric's divine magic as nature magic.
4. The thief/rogue is an alternative to the magic-user/wizard, replacing the magic-user/wizard's magical capability with skill-based utility and combat capability. The assassin subclass focuses on skills used for ambush and subterfuge.
5. The monk is an alternative to the cleric, replacing the cleric's divine magical capability with "thief-y" skill-based capabilities.
The gestalt of 2 and 4 is the magic-user/thief multiclass, expressed in 5E as the Arcane Trickster archetype.
The gestalt of 1, 3, and 4 is the fighter/cleric/thief multiclass.
6. The bard is an alternative to the fighter/cleric/thief, replacing clerical divine magic with druidic nature magic and bardic musical/oratory magic.
This suggests a few questions to me. First, why are there no full-time casters equivalent to the magic-user/wizard for other types of magic? And second, might it not be a good idea to name and define archetypes for other multiclass combinations the way 5E did for the Eldritch Knight and Arcane Trickster, and perhaps break them out into their own classes as seems to have been done for the cleric and bard?
