It may not have been space decreasing, but popuilation increasing.
When you visit a zoo, what is it that you most want to see? Cute babies! A zoo or safari park without babies is a sterile environment for beasts and visitors alike. The ethos these days is to make sure that the animals live as close as possible as they would in the wild, which includes mating and producing young, but that needs to be controlled.
Cuddly creatures are very nice for all, but babies have a habit of growing up, and what do you do with them then?
Keep them? you'll need more space, and you'll need to keep them away from their parents if they are likely to have fights, or breed incestuously.
Send them to another establishment? If it is a rare and attractive specimen, they will be grateful, but not if it is yet another of something they already have enough of.
Euthanase them? Only if you want to be on the front page of the daily papers.
Feed them to the lions and tigers? Imagine the headlines!!!
One of the funcions of BIAZA and the other associations is to be a kind of dating agency for zoo animals. They keep studbooks with the ancestry etc of all the animals in collections, and advise on which should be allowed to breed, and with which mate. This prevents close interbreeding, and warns if one species is becomeing over-represented so breeding should be completely stopped for a while. They also oversee the movement of animals from one zoo to another, as well as their husbandry.
So pleas support zoos and wildlife parks which are members of BIAZA, and boycott ones which are not.