Could this be Dacey’s Patent Automatic Nanny by Ted Chiang?

The story concentrates on different emotional relationships that humans develop with machines. Reginald Dacey argues that a mechanical nanny is much better able to raise a child than a human one. At first, society accepts the idea and many families buy automatic nannies, but when one malfunctions and kills a child, people lose interest. Dacey attempts to prove the machine is still safe by using the machine to raise his own child, but no one is willing to be the child's mother. When his son Lionel finally adopts an infant and raises it exclusively using the automatic nanny, the result is a child who is only capable of interacting with machines and not humans.

There's a mention of Babbage in the opening paragraph

Reginald Dacey, a mathematician born in London in 1861. Dacey’s original interest was in building a teaching engine; inspired by the recent advances in gramophone technology, he sought to convert the arithmetic mill of Charles Babbage’s proposed Analytical Engine into a machine capable of teaching grammar and arithmetic by rote.

This is Dacey’s Patent Automatic Nanny by Ted Chiang.

The story concentrates on different emotional relationships that humans develop with machines. Reginald Dacey argues that a mechanical nanny is much better able to raise a child than a human one. At first, society accepts the idea and many families buy automatic nannies, but when one malfunctions and kills a child, people lose interest. Dacey attempts to prove the machine is still safe by using the machine to raise his own child, but no one is willing to be the child's mother. When his son Lionel finally adopts an infant and raises it exclusively using the automatic nanny, the result is a child who is only capable of interacting with machines and not humans.

There's a mention of Babbage in the opening paragraph

Reginald Dacey, a mathematician born in London in 1861. Dacey’s original interest was in building a teaching engine; inspired by the recent advances in gramophone technology, he sought to convert the arithmetic mill of Charles Babbage’s proposed Analytical Engine into a machine capable of teaching grammar and arithmetic by rote.