In American English, shouldn't "gotten" be used as a part participle? [closed]

I live in the US. I sometimes hear some Americans say

I haven't got a response yet.

This sounds wrong to me; in American English (unlike British English) one would say

I haven't gotten a response yet

You would only use "have got" as in the expression "to have," e.g. I've got a few seconds, but not in the past-participle form, which is a key difference from British English.

Am I correct?

As I've said before, several different times, this is a very complex topic, with a lot of different threads woven together. Viz,

1. got versus gotten, as past participle of get
2. get as the causative/inchoative verb for both be and have
3. have versus have got (or just got), all meaning 'possess'
4. modal idioms like have to 'must' and get to 'be allowed to'
5. constructions like be/get married/tired/sick, have/get it done/fixed, get/bring him a beer,
   among others

The basic rule in American English is that one does not use got to refer to acquisition, but rather gotten. Hence

• I've gotten the flu

means that I just caught it and refers to the acquisition process, whereas

• I've got the flu

means that I am now ill with the flu, having caught it sometime prior.

All of the idiomatic uses of get take gotten in American English.

• He's never gotten {the big picture/his taxes done/me a beer/anybody killed yet}

but not

• *He's never got {the big picture/his taxes done/me a beer/anybody killed yet}

in American English, at least.

In American English, have got is an idiomatic construction meaning have or must:

I’ve got a cat. (I have a cat)
He has got to go. (He must go.)

This is different than the standard present perfect, which uses the participle gotten. Have gotten means something like have received, have obtained, or—when it functions as a linking verb—have become:

I have gotten a letter. (I have received a letter.)
He has gotten a cat. (He has obtained a cat.)
They have gotten ill. (They have become ill.)

With its yet, your sentence would most naturally be expressed as:

I haven’t gotten a response yet. (I haven’t received a response yet.)

Still, in other configurations, an argument for have got could be made:

I’ve got only ten responses to work with here; that’s not enough data! (I have only ten responses to work with here; that’s not enough data!)