Why do people think it costs hundreds of pounds to register your child's birth?? It's $65 which is currently £38. Granted if you also go for the passport at the same time, that adds @£46 ($82), but it's not hundreds (plural) to do so. It's actually a good time to do so because of the exchange rate, which means you're paying @£84 - less than a hundred. If you get a SSN for your child at the same time, that's free. And yes, the British passport for children is cheaper (£25). But I can't imagine telling your child that you skipped American citizenship because it was cheaper to be a Brit! (Obviously there are more reasons than that, but that shouldn't be the primary one, I don't think).
Oh, and the photographs are the same for both passports, usually you get four which means that you are only paying once if you get them done right the first time, and at least in Belfast there's no shortage of places that do passport photos. Snappy Snaps was the best one, just put the baby on a white piece of paper on the floor and no fiddling about with holding the baby's head up or making sure fingers are out of the way.
If you are intending for your child to have a choice which includes the option of being an American citizen, and you plan to travel to the US before the child makes that choice him/herself, you will have to fork out the dough to register the birth and get the passport to conform with the law. If you don't want them to have the choice, then it's fairly simple. They aren't Americans, and will never make the choice themselves. For when they are of age and look into getting an American passport, and it's shown they have travelled into the US on foreign passports, they won't be able to.
Immigration laws being what they are, and politics being what they are, I am in the camp that avails of all available citizenships for my kids while they can, and let them sort it out in the future if they are inclined.
But it does seem pretty simple. If you want your child to have a choice, you have to do the paperwork and follow the law for travel into the states now. If you are making the choice for your child, and that choice is to not have American citizenship, you don't bother with the American paperwork or passport and your child will never be an American citizen. Your child should still be able to travel to the states on holiday as any other British citizen can, and if they wish to settle there they will have to follow the same immigration procedures if you have opted for not recognizing the American option.