So I did more digging around in all of my rulebooks, and here's what I came up with. (I don't have access to
every book published by Wizards of the Coast for D&D 5E, but I do have a lot.)
- There are 5 classes that always gain the Extra Attack feature (Barbarian, Fighter, Monk, Paladin, and Ranger.)
- Of these 5, two of them also gain the Spellcasting feature (Paladin and Ranger)
- None of them are "full" casters (able to cast cantrips thru 9th level spells.)
- The Fighter can gain Spellcasting, but only by choosing the Eldritch Knight subclass.
- Only the Barbarian and the Monk never gain the Spellcasting ability through subclasses or other class options.
- There are 4 classes that can gain the Extra Attack feature by selecting certain subclasses and/or class options (Artificer, Bard, Warlock, and Wizard.)
- All of them have the Spellcasting feature (or the Warlock equivalent, Pact Magic)
- The Bladesinger (wizard subclass) is the only option for a player that that wants Extra Attack and full-caster Spellcasting.
- There are 4 classes that can never gain the Extra Attack feature, regardless of subclass or other options (Cleric, Druid, Rogue, and Sorcerer.
- Three of them are "full casters" (Cleric, Druid, and Sorcerer.)
- About three-quarters of all classes (9 out of 13) can gain Extra Attack, almost all classes (11 out of 13) are able to cast spells, and more than half (7 out of 13) can do both.
Conclusions that we can draw from this:
Extra Attack is not a "martials only" class feature. All classes have access to Extra Attack or Spellcasting, and most classes have access to both in some way.
Extra Attack isn't consistent across the classes. Different classes gain it at different levels, they gain it with or without subclasses, and non-casters, half-casters, and full-casters all can get access to it.
Classes that gain Extra Attack as a class feature (independent of subclass) typically gain it at 5th level. Classes that gain Extra Attack as a subclass feature typically gain it at 6th level.
Without this feat, the only way a Cleric, Druid, Rogue, or Sorcerer could gain the Extra Attack feature would be to multiclass with one of 9 other classes that grant it. This doesn't incentivize "non-caster" multiclassing, however---Sorcerers almost always multiclass with Warlock, for example.