Honing can and certainly does straighten a hole in a given context. Perhaps there is some misunderstanding or misinterpretation of what happens and of what is being said.
I've used Sunnen hones for align honing the main journals of an engine block. In a nutshell, what you do is take a few thou off of the bottom of all the main caps, creating an egg shapeed bore. Remember, the hole has to be undersize before honing to size. A small block chevy has 5 main caps..Lets say that we have one cap already perfectly sized, round, and centered to the correct centerline of the 5 journals..We'll put that cap in the middle. Now, we have a crooked bore, with the center cap being the only one that is to size and straight..where we want it. If we took a straight edge and held it against the bore surface of all 5 caps, there'd be a gap at the one that is finished. Does everyone agree that we now have a crooked bore?
Now, if we hone the others until they are all perfectly round with the middle cap, we have straightened the bore and corrected any misalignment of the bore. Coincidentally, core shift is the biggest reason this happens with cast iron engine blocks after going through many heating,cooling cycles, then unbolted, relieving the stresses being stored in the block.
If we can agree that we have straightened the bore of the main journals, we should now be able to agree that honing can and does straighten a bore..but it must start out undersized and hone to size. Straightening the hole is the result. This process really has nothing to do with the od of the caps or block, and so, has nothing to do with the od of a barrel, either. So, what Butch says is true relative to the bore not being centered with the od. But any crook, kink or curve in the bore, theoretically can be honed out...within reason, of course, and depending on how much under size the hole started out and how much it takes to both end up straight and to size. Hopefully, we can all agree as to how honing can and does straighten a hole in this context.
Now, as for the benefits of honing the bore...There are pro's and cons. First, too smooth of a finish doesn't reduce fouling..it makes it worse. It also matters as to how the barrel is to be rifled..be it cut or buttoned. To my knowledge, with cut rifling, the only down side would be the potential for more fouling IF not lapped well after rifling. Of course this is not the case with most premium barrels and it would only affect the top of the lands..that are already to size when the grooves are cut.
But on button rifled barrels, the force needed to push or pull a button through the bore of a finely honed bore is not less, but much, much higher. I can only assume this is due to not holding lube as well as a less "finished" bore before rifling. Not that it can't be done though..as others have mentioned a couple of barrel makers who are known to button rifle their barrels, also hone the bores before rifling. I believe that it only needs to be factored into what the pre rifling bore dimensions are relative to the finished button dimensions are. I view this much like the barrels that Savage produces, in which many of us are familiar with their infamous "railroad tracks with cross ties", appearance with a bore scope. I opine this as the result of marginal(to put it nicely) bore to button dimensions, in order to reduce wear, tear and stress on tooling as well as speed up production..by the button not fully ironing out the marks left from the drilling operation. Take that FWIW because it's a combination of reasoning and knowing just enough about the process to be dangerous. The pressure to push/pull the button through a smooth vs. less smooth drilled rifle barrel came straight from the mouth of the owner a barrel making company...along with numbers that I don't recall precisely..but it was like night and day, with no other differences other than finish of the drilled/honed hole prior to rifling. Then you have to figure how much the bore with change size during heat treat, too....and that number can change with the batch of steel and the time/temp for heat treat. There's a lot more that goes into making top quality barrels than meets the eye.---Mike Ezell