Limits To Growth did in fact predict a decreasing birthrate. I suggest you look at that graph more closely.

Note that the birthrates on that graph decrease until there is a spike in the death rate - when the collapse starts happening.

Note that the net population continues to fall after that, even with the higher birth rate, because people are simply dying too fast to be replaced.

To prevent catastrophe, we would have had to become zero population growth billions and billions of births ago.