I use them for loading for multiple chambers, same cartridge. Example: 6BR, have 5 chamberings, 2 with identical headspace lengths,(cut with my reamer), 2 others same headspace cut with another one of my reamers, and the fifth cut with my gunsmiths reamer. So, three different headspace lengths to deal with.
Without the shims I would have to constantly change the adjustment(s) on my Redding FL neck bushing die, by re-adjusting the die lock ring, a pain in the a**.
I have the die adjusted for the shortest headspace length, 1.152", and add the appropriate shim for the 1.155" and 1.159" lengths.
Would also work fine for the AR-15 example you used. The sizer die could be adjusted for tighter headspace on a bolt-action 223, and add a .002" or .003" for sizing cases for an AR-15. I've done that also.