I don't have the figures for how many dogs have 'forever homes' at the Dogs Trust because they are not suitable for living in a home environment, but I know it's not a small number.
I know that the Dogs Trust has as its core value that it never destroys a healthy dog. Laudable but maybe not practical. I do support the DT (financially as well as in word and deed), but in truth I would accept the destruction of unhomeable dogs and would prefer that they use the funds thus saved to home more of the dogs that will make nice pets for some family.
I myself rescued from one of the rescue charities (not the Dogs Trust), unwittingly, a dog that was not safe around children. It ended in my having the dog put down before he bit a child. (After much help and work trying to make him safe through training, exercise, occupation and environment.) I have never made as hard a decision in my life, and the whole experience haunts me still.
While the problem is of such a scale that logistics tell us there will be many dogs who won't get homed, no matter what we do, then there should be some triage, whereby dogs with serious problems are either shunted to charities specifically for such dogs (so we can all decide for ourselves whether we want to pay to keep such dogs alive) or are destroyed to make way for nice friendly dogs who will make nice friendly safe family pets to find their way to the front of the queue.