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?
Should I just think of it as an exception or an irregularity?

※. I've already read this link: How often do you use "can('t) have done" structure?
※. One thing added: I looked up 'can' in Oxford Advanced Learner's Dictionary of Current English
      (Third Edition, 1974, A.S. Hornby), and here are the examples:

a. One of the prisoners escaped yesterday; he can/could(=may) be anywhere by now.
b. He's an hour late; he can have been delayed by fog, of course.

Now I'm thinking "can" really used to express speculations about the past,
and the meaning was more or less the same as "could" or "may".
if the interesting affirmative "can" was still alive in some dialects, I'd love to know about them and to know
whether the choice between "can" or "could" might be a matter of lowering possibility in the dialects.

I really want to hear different opinions on this "can".