I'm going to guess that your counter will be "you shouldn't design classes around features"...
No, I would not counter with that at all. There is absolutely nothing wrong with designing a class around 1-2 features. What I would counter with is, "You shouldn't design a class around
this feature."
Some examples of "feature classes" done well:
- Barbarians. Barbarian rage provides benefits (damage resistance, bonus damage) which can be applied to any Strength-based weapons and combat tactics you like. Barbarian subclasses then provide additional "rage boosts" on top of this core.
- Rogues. Again, Sneak Attack is a simple boost that can be used with the finesse or ranged weapons and tactics of your choice. Rogues then get a variety of bonus-action tricks, and Sneak Attack is designed to be compatible with all of them.
- Sorcerers. The sorcerer's defining features are Font of Magic and Metamagic--technically two features, but joined at the hip. These allow you to dramatically boost the power of individual spells, but you still have an array of spell options to use them on.
What makes these classes work is that the "single feature" builds on the general mechanics available to all martial PCs (barbarians, rogues) or all spellcasters (sorcerers). It can piggyback off the options built into those general mechanics--it isn't trying to replace the entire Combat chapter.
A less successful "single-feature" class in 5E is the monk with Stunning Strike. Monks are more restricted in their choice of equipment than either barbarians or rogues--a handful of weapons, no armor at all--and Stunning Strike dictates very repetitive tactics: Pick a big threatening creature, blitz it with stuns until it stops moving, then watch your allies whale on it. And because few other uses of ki can compare to SS, a lot of secondary monk features are a waste of space.
And then we have the warlock and EB. EB is even more restrictive than Stunning Strike: No choice of weapons, no choice of spells, not even an option to switch between ranged and melee. You make X ranged attacks for 1d10+Cha force damage each, end of story. It combines with nothing (except
hex and multiclass cheese), layers over nothing, it stands completely alone in the system. You can't customize it except with invocations, and your options there are very narrow.
That is why I consider the reliance on EB to be a bug. It doesn't make the class unplayable, but it limits the options available more than it should.