I think my 7yo visualizes the number line in their head when there's no paper around, but they draw it out in school. I personally don't understand that method, because I always learned to do it like this:

 7372
+ 273
=====

And add by columns. With a number line you add by places, so left to right (starting at 7372, jump 2 hundreds, 7 tens, and 3 ones), whereas with the above method, you'd go right to left, carrying as you go. The number line method gets you close to the number faster (so decent for mental estimates), but it requires counting at the end. The column method is harder for mental math, but it's a lot closer to multiplication, so it's good to get practice (IMO) with keeping intermediate calculations in your head.

I think it's nonsense because it doesn't scale to other types of math very well.