like that of + possessive noun [duplicate]

I came across this sentence:

"His memory was like that of a baby."

I was wondering why the possessive "baby's" wasn't used and why "baby" is acceptable whereas the possessive form is required in this sentence:

"Ian's car was like that of his."

Solution 1:

The possessive is acceptable in your examples, in which case they mean

His memory was like a baby's memory.
Ian's car was like his car.

However, English accepts the so-called double possessive in which this elision doesn't apply:

She is a friend of my sister's.
John is a fan of hers.

It's redundant since of, -'s, and possessive pronouns all signify the genitive, but language isn't necessarily logical. The form has its use in distinguishing

A picture of my family

which is a portrait of your relatives and

a picture of my family's

which is a picture your family owns.

We generally reserve the doubled possessive for human beings, like babies and sisters, but not otherwise. No one says

the founder of the country's.