In the last 2 months back-orders have eased, "seconds" sales occurred, and I ended up with 3 new planes. I sold a few, too, but that's not my question.

Because it's winter here and uncomfortable in my garage workshop, I bring my hand tools inside and overhaul/oil/sharpen etc.
I decided to flatten all my Stanleys' irons backs; The 6 was fine, the 8 (series 4) was grossly not flat and took hours to even get 80% flat and shiny, and the 3 was OK.
I did the cap irons as well a la David Charlesworth.

Why confused? My new planes.
I expected to have a lot of work on the Stanleys, but not on the new irons.
The planes: LV Custom #4, Custom #5 and Skew rabbet (rebate) planes. 2 bevel down, one bevel up (Skew plane).

The sheet that comes with the planes says that the backs are lapped and that only the secondary bevel be needed.
I have 3 DMT diamond plates I use for sharpening, which I assume to e dead flat, unless my square's flatness is suspect. Besides, when doing the primary and secondary bevel, I don't see any lack of flatness.
But each back I try to flatten shows the left and right sides going shiny well before I can get the middle to the same degree of polish.
I'm really not sure if it makes that much difference, so I'd like to rely on opinions here.
"Everyone" seems to opine that flattening the back of older irons is a good thing; modern manufacturing techniques get the irons much flatter than ever before, and I do understand that even these level of instruments are a starting points.
So my question is, with modern,"local" quality tooling, is the need to flatten the back still as necessary?