1)Are pistol grips that bad? If so, why do people use them?
Unequivocally, yes, they really are that bad.
People use them because they think that looking cool somehow translates to effectiveness.
2)Can accuracy be achieved with a pistol grip?
Put enough time into anything, and you can achieve impressive feats. There's video of Bob Munden hitting a balloon with a snub-nosed .38 special at 200 yards. That doesn't mean that a snub-nosed .38 is a better choice than a rifle.
3)Are there any other advantages to a pistol grip besides looking cool?
There's an argument to be made that the lack of a stock makes them much easier to stow and use in a tight space like a car, or reduces the amount of weight you have to carry if you intend to do some serious back-woods hiking. Some advocates for PGO shotguns will also claim that these guns are more easily maneuvered in tight quarters, like the inside of a house.
I would argue that the functional penalties* that a stockless shotgun incurs are much worse than having to put up with either of those disadvantages. If space/weight is
really that much of a concern, you're probably better off jumping through the hoops to get an SBS, or use a pistol or bullpup shotgun or rifle.
*Off the top of my head:
1.) Inability to aim them accurately and
with consistency.
2.) Slower to cycle.
3.) Slower transitions from one target to the next.
4.) Inability to use many kinds of ammunition due to the excessive recoil.
5.) Gaining proficiency requires that you invest much more time, energy, and ammunition than with a properly-stocked gun.
6.) Successfully aiming a PGO shotgun from an odd position that you haven't practiced (prone, rollover prone, at a target that is markedly higher or lower than you're used to, or through an oddly-shaped or small port) is much, much harder to do than with a properly stocked shotgun.
7.) An excessive penalty against being able to make rapid, accurate hits at further ranges** with slugs.
8.) An almost complete inability to hit flying targets***.
**Yes, I've seen the Hickock 45 video, and am aware that it can be done, but clearly not quickly, and certainly not without a lot of practice.
***Yes, I know, your PGO shotgun isn't for trap shooting. It doesn't change the fact that removing the stock also removes your odds of hitting a bird, be it clay or otherwise.