My experience of looking for a rescue pup last year was that the vast majority of rescue places are full of teenage dogs that owners have failed to train and/or socialise properly and elderly dogs that have been cast off when families can't be bothered with them any more.
As LtEveDallas said upthread, there was only one litter of pups in their rescue out of 27 dogs in total.
Back yard breeders and puppy farm are responsible for the majority of dogs that end up in rescue. Dogs are overbred and sold to anyone who wants one, regardless of whether they are suitable for the breed - or even to own a dog in the first place. Yes, unplanned litters do happen, of course they do, but they are by no means the largest part of the UK's massive shortage of rescue spaces.
Fwiw, if my unneutered male ever did manage to get to bitch in season, I would support the bitch's owner in whatever they wanted to do, be that terminate or go ahead with the litter and find the pups good homes - and of course I would share the cost whatever their decision.
Unplanned litters, for the most part tend to be from dogs and bitches kept in the same household or dogs that are allowed to roam free. They are generally the result of irresponsible pet ownership. People who have done a great deal of research, spoken to their vet and made an informed decision not to neuter do not fall into that category. They are far more likely to spend time training their dogs to a high standard and ensure that they are kept under control at all times than people who simply can't be bothered or won't neuter because it's depriving a dog of it's maleness or similar nonsense. 
That isn't to say that it couldn't happen, obviously there are people on here who have had experiences of males going to great length to get to bitches, but I have had and been involved with dogs for 25 years and it has never happened to anyone I know personally, so, at least in my area, it can't be all that common.