BPC should always be on. IF it isn't needed, nothing happens. If it's needed, something good happens (the black compensation is applied). Now if you have a profile that doesn't need this, having it off will be OK, but having it on and sticky makes more sense.
Andrew, I'm not sure you are correct about BPC never does any harm. It seems at least in PS's implementation of BPC, the compensation is being applied by checking the chosen ICC printer profile for what maximum black is reproducible and then scaling the image tone curve from that value whether the image contains those dark values or not. That's not the same as evaluating the image content to see if the actual image has any shadow or black values that would require some compensation to stay within the chosen printer/ink/media color gamut. In other words BPC behaves like a variant of an ICC profile Look up table rather than a variant of a "smart" CMM.
Try this softproofing test. Use a profile like HnPHoto Rag for your printer. It will be able to reproduce gray values down to about L* = 18 without any need for BPC. Now create a gray ramp that stops above that value, say sRGB =50,50,50 which renders L*=21. Since all is in gamut within this image, BPC should do nothing. Yet, on my screen it lifts (i.e., compensates the gray scale) as if full RBG 000 black is also present. Hence, dumb CMM not "smart CMM".
Where turning off BPC becomes useful then is in the occasional high key/lower contrast image or painting reproduction where all is within gamut for the paper without requiring any further compensation to bring colors and/or tones into gamut. In those instances, RelCol without BPC will a better choice whereas Perceptual and Relcol w/BPC will attempt to lower the image contrast somewhat further to make headroom for additional deep colors and tones that aren't even in that image. Again, it's a "dumb" CMM versus "smart" CMM issue, and until modern color management gives us a truly smart CMM, having both BPC and no BPC available extends our rendering choices (i.e., perceptual, relcol, relcol w/BPC, and abscol) in a useful way.
Where I agree that BPC does nothing in PS is when checked on along with use of perceptual rendering. In that instance, the vendors' perceptual tag secret sauce has already accounted for the necessary black compensation so BPC does nothing.