When talking about possibilities in the past, You often use "could have done".

"She could have gone to the theatre with him."
"He couldn't have done such a thing!"
"I could have saved them."
"You could have borrowed the car from him."

I understand "can have done" is used in negative and interrogative statements.

"She can't have eaten all the food."
"Can he have told them all the secrets?"

But I've not seen an affirmative sentence like,

"She can have gone to the theatre with him."
"He can have told them all the secrets."
"I can have saved them."
"You can have borrowed the car from him."

Why is it? As far as I know, "can" sometimes refers to possibilities as follows.

"It can be boiling hot in summer."
"She can be nasty."

Did "can have done" in affirmatives used to exist before?
Or is it still possible but only used in limited contexts?
If it is, when do you use the structure?
If it's not used at all, what do you think is the reasons?

※. I've already read this link: How often do you use "can('t) have done" structure?