Well, the issue with blue is that the eyes behave weirdly with it. Blue can be very annoying sometimes (look at blue LEDs) and can also increase the perception of haziness. Yellow (incandescent) lights are generally better accepted, but they "look old" which is why they make the blue-tinted bulbs these days, to help reduce the yellow-ness of the bulb and make it "look" whiter. Ideally, pure white would be best, of course, or something slightly less blue (which ends up being yellowish, as you have deduced).
HIDs are just as you described - high intensity. When focused and directed properly, they work great (projector style). However, when people pop HID lights into an incandescent reflector assembly, they simply piss off the rest of the drivers since they are not properly directed...
You are also correct, "looking white" doesn't mean brighter, though many people will buy the marketing. As a side note, in some countries they will put a blue-dye in their "bleach" to make white clothes look whiter. Again, it's not really whiter or cleaner than regular soap (since there is no bleach in there at all) but it fools the public well enough, and it's cheaper to make than bleach...