And they also have been replaced by Exterminators, who take care of all sorts of "pests" and insects usually with poisons or traps.

Poison and traps were in wide use at the time of the photos in question and had been for some time.

The only reason that "ratcatcher" is a job that no longer exists is because it changed names to "exterminator", the same way that "secretary" no longer exists as a job and is now called "administrative assistant". Preferred titles have changed over time, but the basic job of killing rats absolutely still exists.

My mother's a secretary

At least in my neck of the woods, a rat catcher's job is primarily monitoring. The rat catcher will trap and bait, but if fumigation is required, they'll call an exterminator.

Is there a reason why using cats is not effective?

I've seen rats bigger than your cat! Also, cats aren't always in the mood.

Its not like rats aren't around any more.