Well that's perhaps a failure on my part because I really wasn't trying to be: I was trying to ease your mind on this one particular point and offer something beyond what you'd received from the other commenters who appear to disagree with you, since they didn't appear to have convinced you that it's okay to let this one thing go and save your energy for other fights.
If it isn't too upsetting, since "refrain[ing] from principled argument [...] is one type of liberalism", I will give one more explanation of my thinking and then leave it at that.
When describing things that are knowable and positive, scale is described upward and outward: "greatness"; "grandeur"; etc. By contrast, depth is typically used to describe attributes that are unknown or negative: "deep feelings/belief/faith/conviction"; "depth of their depravity". And "sheer" is often coupled with "hubris".
If America's unusual greatness is intended, then "the sheer depth of American exceptionalism" is indeed striking, since its form implies the opposite. If the writer means the sheer depth of faith in American exceptionalism, though, then the form is instead quite mundane. I find that mundane usually explains more than striking.
However, I do agree with what you write about deniability: this construction does allow readers who genuinely believe in exceptionalism to carry on unchallenged. But regardless of what you or I think journalists should do, that is the actual job of The New York Times, isn't it?
Between them E, T, A, O, I, and N hold the majority of letters in texts. These are the upper class.
Throwing in the S, H, R, D, and L bourgeoisie accounts for more than three quarters.
This leaves C, U, M, W, F, G, Y, P, B, V, K, X, J, Q, and Z to share less than one quarter of the written letters in English.
I'm not sure that the obvious word of the proletariat needs to be used more, though.
How about syzygy?