I've tried to wade through this thread and have to say that I'm grinding my teeth in frustration regarding the OP. And I'm getting 
. My credentials in rescue aren't quite as strong as Vals, but I've been heavily involved in cat rescue both locally and nationally for over 15 years, fostering/rescuing/trapping/you name it and now work with a specialist dog breed rescue. (Border collies). I am married to a farmer and could concievably have "all the rescue animals I wanted" because we have the space. But I don't. Because to look after them costs MONEY. Food, vets bills, routine care, etc.
Also, a responsible rescue will always, always home check. (And in the case of the one I work with even if they know you well - it's done by an independent volunteer who doesn't know you.) Why? A good case in point with me, was I had to put a piece of fencing up between me and my neighbour as my wall was only 3ft high. I then had to send pictures that I'd done it, to the rescue, before they would even entertain me even meeting a dog. They then identified 2 or 3 dogs they would consider a good match for the home I could provide, and I went to meet them.
All I got from that rigourous process, was the feeling of how much that rescue care about their dogs and their welfare. (But then they were preaching to the converted with me anyway).
I've had a couple of people I've rung up for homechecks for that rescue, who have either been really snotty to me on the phone, telling me quote not to bother them anymore as they had another dog from a rescue who didn't homecheck quote (Massive big red flag to me, as a rescuer actually), haven't returned my calls to arrange a home check, and various other reasons.
Someone once told me that I was unreasonable to insist on homechecks for my foster cats and that I'd get more homes and help more cats. To me, if even one of my foster cats ends up in an unsuitable home, that's not a statistic I'm happy with. Sure, when I do homechecks occasionally, people lie, and it doesn't work out for whatever reason and moglet comes back to me, but the rigourous procedures I have mean that I keep track of my kids, and that's what the rescue animals are to you. Your kids. You invest time and emotion and care and at the end of the day, the whole object of the exercise is to not have them bouncing back into rescue and for them to end up in their forever home.
Floss my collie that I got from the rescue I mention - she still messes in the kitchen at night, probably 2-3 times a week, she can be a little sod with food thievery, she can be skitty and spooky for no reason, she occasionally chases the moglets (but more often than not she's in bed with them), and she is generally being just a dog. She also tried to break out of the garden, but couldn't because the rescue had insisted that I fix my fence before I adopted. Had she got out, she would have only got next door into my neighbours garden, but my neighbour could easily have let her out and she would have then got onto the road. Floss is in a working home, and she is blossoming. All because I was matched to her PROPERLY. Her homecheck took 3 hours, and the adoption took equally as long. What it did mean, is that I could ask all sorts of stupid questions, and the homecheckers and Wiccs could give me a lot of advice.
Cara, my other collie, OTOH, came from a well known rescue, who yes, did a homecheck, but it lasted 10 minutes to check I had a garden. The fence was in the same state as it was when I was told by the second rescue to fix it. I was lucky. I know several people who have ended up with the wrong dog via them because of poor adoption procedures. I also know several rescues who don't do proper follow up and give appropriate support. (And would be quite happy to name them in a PM and why they are bad).
Yes, good rescues may help fewer dogs by people getting annoyed at the homecheck, but my argument is that if the adopters are not happy about the "invasion" as they see it, then they are not the right home.
And as for back-yard breeders... DO NOT get me started!