The primary motivation is in proving overflow facts. Particularly, overflow facts for loop induction variables. SCEV gets many of these cases today, but there's no reason LVI shouldn't get them to and having LVI able to catch the simple cases makes our pass order less fragile.
Note that this patch is only the analysis changes. A separate change will build on top of this to actually make "add" instructions as nsw/nuw.
I wouldn't put all this logic here. Instead, it is easier to do:
Later you can improve precision by making RHSRange more precise.