Backing on Spinning Reel
Backer had two purposes. To put a small amount on the spool so that your super line does not slip on the spool, and to fill the spool because typically super lines are much smaller in diameter than mono.
I do put backer on my trolling reels even though I use mono. The reason being is a trolling reel may hold 450 plus yards of say 10 pound test. Well when its time to replace line, no reason to replace 450 yards when perhaps on 200 of it has ever seen the water. So I will use some discount line for a filler or backer on my trolling reels.
I assume we're talking mono backing for braided line; I agree that there's no particular benefit to backing straight mono (although I have had customers ask for mono backing for fluoro, just to save on the cost of the flouro!).
Beyond that, count me as X3 RE the consensus, it doesn't make any particular difference, although it can be a bit easier to have the line diameters a bit closer to matchin to ease tying, i.e. backing 8lb braid with 40lb mono can be a bit awkward).
My braided reels have mono of close diameter; it does help if you use uni-uni.
I mostly use flourocarbon for leaders; however, I spooled up an ultralite reel with berkley flouro a couple years ago, and the stuff just holds up. In the future I'll probably not put backing on flouro either.