As to whether care in cleaning matters, and whether you notice or not, here's a Canon (rangefinder) lens I got off an auction site. (I bought the camera, not caring about the lens.) The lens looked good in their photos, that were front-lit; but looking closely shows the cleaning damage. It also shows up much better with light through the lens.
You can still get very nice pictures with the lens, but there is more "veil" if light is shining on it from the front.
I have lenses from the same period that I've had since the early 1960s that I've cleaned with tissue and cotton swabs (after blowing and brushing) for 50 years that still look pristine. Care does matter.
I also don't clean if it isn't really needed. I've seen people automatically wipe a lens as they take a camera out to use, without even looking at it first.
I know recent coatings are harder. I saw a demo where they used a "scotchbrite" pad on a lens and then showed pictures taken with it. (But an insider said they intentionally didn't use lighting situations that would show scratches.)