I agree with you totally mutty. Pounds are not 'rescues', they are holding cells for dogs. If they're lucky enough to get offered a new home, they're sent off with no checks, if not, it's the end of the road for them.
Also agree that true aggression of no discernable cause is very rare. The issue some of the smaller rescues have is that if a dog is surrendered with a bite history, even if they show no sign of aggression at all during their time with the rescue or foster, if they then go on to be poorly handled at some point in the future and end up resorting to biting again, no matter how many ignored warnings they gave out first, the sad fact is that these days many people will sue the rescue, the press will get hold of it and rescues can and do get shut down as a result. As I said, they do everything they can to ensure the dogs go to the right home, with the right type of owners, but there's no crystal ball and in truth all homecheck, assessment interviews and adoption questionnaires are only a snapshot of the potential new guardian's situation at the time of rehoming - no-one can predict the future. Currently decent rescues are still able to choose to support and rehabilitate such dogs, but there's been rumblings about specific legislation regarding prosecution of anyone who knowingly rehomes a dog that's already bitten. That's a scary prospect for any rescue.
I think your view of how common homes like yours are is a little skewed, because you are actively involved in rescue and high level training. I too know of plenty of people that have taken in difficult cases and I have done myself, but in a way, it's similar to the way we're all shocked and outraged when we meet or hear of irresponsible, ignorant people causing no end of problems for their dogs and other people. People like that don't exist in our canine-related social circles, because we mix with those that care enough to give and damn and want to learn everything they can. The vast majority of dog keepers in this country simply aren't like that - they buy a dog, maybe take it to puppy classes if it's lucky and that's that. The working trials, agility, obedience world is only a very select microcosm of dog ownership in the UK and it's easy to forget that those owners are sadly in the majority.
Yes, there are people who can and do take on the difficult cases, but there aren't anywhere near enough compared to the numbers of dogs that are damaged then dumped, you only have to take a look at the long-term cases in some of the better rescues to see how hard it is to find people to take them on. The lucky ones will at least find long-term foster, the less lucky live out their lives confined to kennels and runs, but with their physical needs met and people who genuinely care around them to earn their trust and help them heal their mental and physical scars, but no matter how we dress that up, it's far from ideal.
At the end of the day I think, fundamentally, we are in agreement. Genuinely decent rescues are up against it from all angles on a daily basis, while pounds continue to support byb, overpopulation and throw-away dogs by essentially just selling on those dogs that are victims of all these things.
I am mostly supportive of no-kill shelters, but there are a couple who have had no choice but to pts a dog that even after a mammoth rehabilitation programme and exhausting every avenue available to them, was still totally unpredictable and highly aggressive. In both cases the general consensus, both veterinary and behavioural, was that there was far more going on than just adverse life experience, most likely underlying brain damage or similar. That's literally two dogs, at different rescues, that I know of in over 20 years and knowing how much those rescues care and how hard they work, I would never condemn either one for making those individual decisions. So, as you said, exceptionally rare - but it does happen and some would insist those rescues couldn't consider themselves no-kill as a result.
Floral homechecks, if done properly can tell a good homechecker an awful lot about the potential adopters. Things you may not think about, such as 'Is the house pristine to the point of obsessive cleanliness?' and 'How do the kids behave?' 'Where to any existing dog have there beds and is there fresh water down?' etc can be very telling. Often home-checkers will bring their own dog to the appointment and that can be very interesting in terms of seeing how the homeowner, their family and any existing dogs react to a dog in their home environment (I have heard of cases where the person being home-checked would only allow the home-checkers dog in the kitchen, as they didn't want dog hair on their carpets! 
). It's also amazing what can be gleaned out of just a general chat, you can pick up all sorts regarding dog-owning history and attitudes to keeping dogs that you simply wouldn't get from a rehoming questionnaire, where the owner can be very guarded about what they do and don't put down.