This is going to be a long response.
To deal with your points one by one...
I don’t see what the problem is with not having a pedigree.
I'm by no means obsessive about keeping dog breeds 'pure' (I think for several breeds, outcrossing is becoming an urgent requirement). For many, perhaps most, dog owners, it makes no odds if their dog is pedigree or not, provided the dog has the traits they need for the dog to fit their lifestyle (personality not overly energetic, not prone to resource guarding or guarding behaviours in general, not having sky-high prey drive, being moderately trainable; physically not too big/small, grooming requirements within what they can provide, no major health issues or allergies etc). But one of the best ways of knowing what sort of dogs your puppy is likely to turn into is know its breeding. Its breed, the lines within that breed, the parents' temperaments and attributes. If you have no idea what the parents were like, if they were of no obvious breed (or from breed with which you are not familiar), you have no idea if a behaviour that you see in a young dog is a one-off or an indication that an ingrained, genetically-driven circuit is switching on. A friend of mine rescued a young dog of indeterminate breed from Europe. He turned out to be much, much bigger than she expected, to have far higher prey drive than she was anticipating and to need more mental stimulation to keep him happy than she had planned to offer. Fortunately she has had the time and headspace to provide everything he has needed - but he could easily have gone very badly wrong in another home.
Obviously breed does not set personality in stone, but there is a bell curve. I have two dogs of the same breed with very different personalities, but they both have very high prey-drive, work the wind in very much the same way, and have the breed trait of being good around people and other dogs.
Finally, some people know exactly what sort of dog fits with their lifestyle - or they want or need a dog that they can work. This is where breed is very, very useful. I know precisely what I want to do with my dogs. I know how much fur DH will tolerate around the house. I know how much exercise and mental stimulation we can provide. I know how well I can train a dog. We have a high-energy, high-drive, prey-driven breed, because that works for us. My older dog would be a shit-head in many homes, because if she doesn't get a breed-appropriate outlet, that is what she slowly turns into. With us, she is happy, confident, reliable and trustworthy.
There is a reason why Guide Dogs breed the puppies they need. They don't obsess over purity of pedigree (they use a lot of Lab x GR) but for sure they obsess over the pedigree itself, the health and lifespan and temperament and traits of the dogs whose genes are going into that breeding.
If you love animals and you’d like to add a dog to the family what does it matter.
See above: dogs are different from each other and your circumstances may well dictate what sort of dog will work for you. We see a steady parade of out of control spaniels across this board: not everyone is equipped to deal with the extremes of cocker spaniel traits. And that is with people buying puppies with fairly predictable traits. When somebody living in the suburbs gets a European rescue with loads of energy and strong guarding tendencies (because its 3/4 Carpathian shepherd but came up a bit small and less fluffy due to the other 1/4 of its genetics) things can go very badly wrong.
If you’re choosing to adopt a child do you specifically only specify a type, blond, short nose etc. No. Because that’s wrong. You chose a personality
Actually, when you adopt a child, you don't choose. You get matched.
But aside from that, unlike dogs, humans have not been bred for literally millennia to fix traits. There have been distinct types of dog for at least 3,000 years. Yes, most breeds only became fixed within the last 150 years, but a lot of those breeds developed out of lines of dogs bred for specific looks and, crucially, specific jobs. Again, this is why things go wrong with some working cockers in pet homes: these are dogs bred for generations to hunt and flush, and they need an outlet that plays to those genetic drives.
Apart from that for the dogs sake you make sure you can deal with size and energy levels.
100% agree. But if you get a mongrel (as a descriptor, not an insult) puppy, you might have very little idea of its ultimate size and energy levels. If it was born on the streets, you'll have even less of an idea because you might not even be able to see the mother.
You also need to consider drive: what the dog desperately wants to do. Some dogs need a specific outlet.
A lactating dog on the streets is deserving of a home and love and care just as much as any, if not more given the hardship they may very well have endured.
And did I say that they weren't? The point I was making was that if people don't breed dogs, the only dogs that will be born will be the ones born to feral or straying bitches. And personally, because I love dogs, I'd rather that dogs weren't feral, though I think that a lot of owned dogs who wander the streets (i.e. stray) elsewhere in the world often have very good lives - provided that their reproduction is controlled and the females aren't producing litter after litter.
I find your comments about ‘random bred dogs’ as you call them upsetting and distasteful
What else would you like me to call them? It's a statement of fact, not a criticism of the dogs themselves (who wouldn't understand it anyway). We had an ex-street dog when I was a kid, a delightful, affectionate, happy chappie of no discernible breed. We were lucky that he was so trustworthy and easy.
Finally, I suppose you could argue that we shouldn't have breeds at all and should only have the generic dogs that you see on the streets of Africa and India. That would throw away years of careful selective breeding for specific traits to fit specific lives, and deprive the military, police, Guide Dogs etc of the genetics that they need.
Personally I think having breeds makes the world better for both people and the dogs - because more dogs end up in the correct sort of home than might otherwise be the case. I am very concerned, though, that closed stud books will eventually knacker up breeds as inbreeding levels inevitably rise, so for that reason I'm 100% in favour of outcrossing in a sensible way.