What exactly are the spacers for, correct chainline on a triple chainring setup? If that's the case, can I fit the BB on my singlespeed without the spacers?

No, the cranks are set up for an exact overall BB width so they need the spacers to be there else the cranks will slide form side to side in the BB bearings.

Makes you wonder why the frame manufacturers don't adopt a new BB width to do away with the spacers.

it comes from there being 68mm and 73mm bb shells on frames, plus some with 'e-type' front mechs or bb mounted chainguides. You used to have to buy one of three different 'shelled' cartridge bb's for them there options. I like how one crank and one bb keeps its options open with the spacers.

(until people started making 83 and even 100mm bb shells, bah!)

Because they're are several standards that have been around much longer than external bearings.
However, press fit bb's are getting more popular with some manufacturers, doing away with screwing any cups into the frame, they have a different type of BB cup that presses in like a headset, but gives the same overall width as HT2/X type etc.

Yeah spot on. You need them and they are useful. If you don't use them your bb axle will have some left to right play.

it comes from there being 68mm and 73mm bb shells on frames, plus some with 'e-type' front mechs or bb mounted chainguides.

BINGO

If you have a 68mm BB, you need all 3 spacers.

68mm BB and an E Type front mech, you need 2 spacers

73mm BB and you need one spacer

73mm BB and an E Type front mech you need no spacers

Makes sense to do it this way rather than have several different configuration BB's. After all what do those spacers cost to make? Fractions of a penny each I'd warrant…

Oh, and if you need to run an odd number of spacers, the extra one should always be on the drive side for correct chainline.