The main reason for getting spaying and neutering done is lowering the number of domestic dogs and domestic cats.
One non-spayed female in the street is much more than one or two litters per year. The problem is more complex because you must count on geometric progression (sequence of numbers where each term after the first is found by multiplying the previous with a certain fixed number. For the example, with number 3 where the sequence would be: 2, 6, 18, 54...)
Spaying of females and neutering of males have many more advantages.
Spaying
It prevents occurrence of mammary gland tumour and infection of urinary system. With elimination of hormone signals, you can tone down the temper of the dog which is very important for stray dogs. The owner gets rid of the problem that heat period brings, since by dog etiquette, you should avoid terrain where other dogs walk, and also, it will resolve the problem of tendency of a female dog to run away in that period or possible boosted irritability.
Elimination of hormone signals can tone down the temper of both female and male dogs, which is important for stray dogs, as well as owned ones.
Neutering
It eliminates sex hormone, testosterone. It will reduce aggressiveness and tone down some of the dominant behaviour, such as establishing hierarchy and territoriality, which can even be annulled. It has especially huge effect on aggression and tendency to run away when it senses a female in heat.
Neutered dog many males do not consider as competition, so this way, a chance of a fight is also toned down. It may happen, when two neutered dogs meet, or if only one is neutered, that they express dominant approach or posture, but after the sniff they will start to play.
Neutering will not change fundamental temper of the dog. The older the dog, when neutering takes place, the less of possibility that its dominant trades would be toned down. Neutered male will not be able to reproduce anymore. Erection will still be possible, but production of sperm will be stopped.