What explains the differing levels of acceptability of 'that' in the following examples?
Solution 1:
Since we're always talking about a pronoun here, why not just use the most standard/proper pronouns here and answer the questions as follows:
1Q]: Is E̲x̲x̲o̲n̲ your parent company?.................. [1A]: Yes, t̲h̲a̲t̲ is our parent company. Yes, IT is our parent company.
[2Q]: Is y̲o̲u̲r̲ ̲p̲a̲r̲e̲n̲t̲ ̲c̲o̲m̲p̲a̲n̲y̲ Exxon ? [2A]: ?Yes, t̲h̲a̲t̲ is Exxon. So many things I could say here...but I fear I'll diverge too much. Saying, "Yes, THAT is Exxon" is just a horribly phrased answer in general.
[3Q]: Is A̲l̲e̲x̲ her father?......................................... [3A]: Yes, t̲h̲a̲t̲ is her father. Yes, he is her father.
[4Q]: Is h̲e̲r̲ ̲f̲a̲t̲h̲e̲r̲ Alex? [4A]: ?Yes, t̲h̲a̲t̲ is Alex. Yes, HE is her father.
[5Q]: Is t̲h̲e̲ ̲t̲a̲l̲l̲ ̲F̲r̲e̲n̲c̲h̲ ̲d̲u̲d̲e̲ your roommate? ..... [5A]: Yes, t̲h̲a̲t̲ is my roommate. Yes, HE is my roommate.
[6Q]: Is y̲o̲u̲r̲ ̲r̲o̲o̲m̲m̲a̲t̲e̲ a tall French dude? [6A]: ?Yes, t̲h̲a̲t̲ is a tall French dude. Definitely not an acceptable answer. -- But why wouldn't one answer this way: "Yes, HE is / Yes, HE is a tall French dude.
[7Q]: Is J̲i̲m̲ your name?......................................... [7A]: Yes, t̲h̲a̲t̲ is my name. This answer is actually the most acceptable, for once.
[8Q]: Is y̲o̲u̲r̲ ̲n̲a̲m̲e̲ Jim? [8A]: *Yes, t̲h̲a̲t̲ is Jim. Yes, IT is. / Yes, IT is Jim.
[9Q]: Is M̲c̲T̲a̲g̲g̲a̲r̲t̲'̲s̲ ̲n̲a̲m̲e̲ Jim? .......................... [9A]: *Yes, t̲h̲a̲t̲ is Jim. Yes, IT is. / Yes, HIS name is Jim.
[10Q] Is t̲h̲e̲ ̲m̲a̲i̲n̲ ̲t̲h̲e̲o̲r̲y̲'̲s̲ ̲n̲a̲m̲e̲ Bootstrapping? [10A]: *Yes, t̲h̲a̲t̲ is Bootstrapping. Again, why not just use the proper pronoun? It's a pretty long explanation to write out the reason(s) behind why using "that" and "he/it/she/etc." are different, bust just think of all the instances in which you would use "that" as the most acceptable/proper word. "That" tends to have a distance to it; that tends have the sense of being "other" (if you get what I mean by the phrase "being other"). And then, of course, when referring to other types of pronouns, "that" just doesn't work at all.
Bravo for an interesting question though. I do hope that someone who not as lazy as I am will come around and explain it in further detail, but I have it's Friday evening and I'd prefer to be eating dinner than sitting here and continuing to go down this rabbit hole. Please don't feel ill will towards me for THAT -- haha!