I have two rescue dogs (rescued on two different occasions from two different locations) and I volunteer for a local rescue organization. Yes, some of the stipulations you mentioned are unreasonable (the smoking one specifically), the no children is not. We have several WONDERFUL dogs right now that simply can not be adopted to households that have young children. They would end up accidentally harming the child by knocking it over when the pup got excited. They are not saying anything negative about you, simply that the particular dog you are interested in isn't good with children.
Most of our applications are evaluated on a case-by-case basis, depending on what is needed for the dog. We've had to turn down some great homes to particular dogs because the family and the dog didn't match well, but we always tell them we'll consider them for [insert select few dog's names here] now or other dogs that don't have those specific problems in the future (or refer our approval to a nearby shelter that has dogs they might be interested in).
Our rescue application is about 4 pages long, and must include references (3 non-family), the name of the vet you plan to use, and your landlord if you rent (and we DO CALL). The shelter I adopted one of my dogs from, required a written letter from your landlord stating they approve that specific pet, and their restrictions (be it weight, or breed). My German Shepherd was from a (kill) shelter and only required a copy of my drivers license for their records (proving my age and that I did adopt the dog)--he was $50.
Some dogs DO need fenced in yards, others don't tolerate other dogs or cats, and some don't like children--just like people have varied personalities and characteristics so do dogs. My GSD and my Border Collie would never do well with a family not interested in extensive training. A Pug we currently have in rescue would do horrible with someone who was very active, since it's older and on the lazy side, but we still had a marathon runner who wanted a dog they could run at least 5 miles a day with put in an application on him. Once the adopter realized what they REALLY wanted in a dog, they knew the Pug wasn't for them, and ended up with a younger active breed (I believe a border collie mix), and they are very happy together.
I personally would never put a Husky in a home without a fence, a Border Collie or other active working breed with a young busy family, or any dog with someone who lets them run free on their property or in the neighborhood (off leash sometimes for play and training is fine).
ADD: most of the places to find dogs in my area are one of two types: a shelter/pound or a rescue organization. Lucky for us the shelters in my immediate area are non-kill and therefore a little more selective of who adopts their animals. The rescues are VERY particular and if you want the dog they want to KNOW it's something you've thought through and aren't just mesmerized by the puppy face. This "wait period" allows people to make an educated decision as to what they are getting into and the commitment involved, instead of a "he's so cute"mentality.
The more applications locations get the picker they can be about the placement of their dogs. The GSD I adopted was in a kill shelter and they had NO application, just a donation was all that was required. These agencies don't WANT the dogs to get euthanized, but instead are trying to maximize the probability they truly are going to a good home, and won't be rehoused in a few months when the family decides they can't handle having a dog.
I believe your area is probably a little to picky if it IS a kill shelter, since these dogs have a limited life in that shelter. As someone else mentioned, they may have a transfer program that allows the dogs to be moved from one shelter to another in hopes it finds the perfect home (my Border originally came from a shelter in KY).
Rescue worker; owner of two rescue dogs.