Again, it’s always easier to add than subtract.
I think this claim is obviously false.
Here are some examples where it is easier to subtract than to add:
* If you want a game with scene-based conflict resolution, the game has to be built around that possibiilty (even when it is, look at the trouble 4e had in getting the maths right!). Trying to add this sort of mechanic into a game not designed to support it from the get go is not at all easy. If the option is built into the game, though, it is very easy to ignore for those who don't want it - the Burning Wheel books make the point, for instance, that not every game of BW has to include every complex resolution system in the rulebooks.
* If I want really fun dragon encounters, that are mechanically workable, capture the traditional flavour of a terrifying, fire breathing wyrm, and that won't devolve into stunlock vs dragon, then I probably want professional designers to design my dragons, and perhaps also to design other elements of the system so as to make those dragon encoutners viable (again, look at the trouble 4e had getting dragons right). If someone doesn't want to run dragon encounters (and I'm to some extent in that category - I don't hate dragons, but I much prefer demons and undead) then I just ignore the dragons in the monster list.
No doubt there are some different instances where it is easier to add than to subtract. But that is not at all a general truth.
But when subtracting something from the game it’s less obvious what the effects will be or if you’re forgetting anything.
Subtracting dragons from my game isn't going to have any unintended consequences that I can see. In 4e, the consequences of subtracting the cleric from my game are clearly spelled out - if the players want a leader they'll have to build a warlord, bard, shaman or ardent. And in AD&D, nothing at all is going to happen if I subtract half the polearms on the weapon list. (Even subtracting the longsword probably won't have any non-obvious consequence.)
I'm sure there are some cases where subtraction can have unforeseen consequences, but I don't think there is any reason to think that it generally will, or that those consequneces will be any more severe than the unforeseen consequences of adding things (look at all the warnings in classic D&D, for instance, about adding new spells or new items - the designers clearly thought that adding that sort of stuff could be potentially gamebreaking).
Warlords are not the only example of inspirational healing in 4e. Once it made the decision that hitpoints would not be health there was second wind and various other non-magical healing. So taking out the warlord doesn’t solve the problem because you also need to remove second wind, which means you need to find a new dwarven racial power. And there are feats and powers tied to second wind and dwarves and warlords.
The feats are neither here-nor-there - 4e has so many feats that the game would survive the excision of a dozen or so of them. But you are correct that trying to remove inspirational/martial healing from 4e would be a near-hopeless task.
But adding is finite. You’re taking a self-contained addition such as second wind, inspirational healing, and the like and adding it into the game.
The idea that you can just add inspirational healing to a game designed without it and have it all work smoothly strikes me as pretty optimistic. As you yourself have pointed out, making it work in 4e involves embedding it into the systems from the ground up.
The origins of the Avenger class come down to needing a divinestriker.
It’s unique defining mechanic is basically Advantage.
It’s flavour paints it as an offensive paladin or aggressivecleric. “Divine assassin” isn’t a class, it’s a character, a narrow archetype.
I don't really see the reasoning whereby mystical assassin is too narrow to be a class, but armour-wearing priest of the Knights Templar variety - ie the traditional D&D cleric - is not. The divine assassin picks up a good chunk of the monk archetype (which Monte Cook tackled in AU with the Oathsworn), plus the religious zealot idea as well, which I think has a reasonable degree of popular currency.
And the unique defining mechanic for the classic D&D cleric is healing and turning undead. I'm not seeing how that's radically broad compared to the avenger's movement and Oath of Enmity.