Consider the following exchange:
 Q: Is your name Jane?
Aa: *Yes, it's right.
Ab: Yes, that's right.
Note that [1Aa] is simply not acceptable. It's not just that that is preferred to it; it's rather that, in Standard English, it simply cannot be used here.
Yes, in the replies [1A], the reference is clearly (supposed to be) deictic rather than anaphoric (see below); and the characteristic usage of 3rd person personal pronouns he/she/it/they is anaphoric. But they certainly can function deictically at least sometimes; CGEL gives the following example (p. 1469): Isn't she lovely! (uttered while looking at someone's baby).
So why is [1Aa] completely unacceptable, rather than just being less favored than [1Ab]?
I am well aware that Yes, it is would be completely acceptable... and I do understand why it would be. But [1Aa] is not, and my question is specifically about why it is not.
Some background on deixis
[1Ab] is a clear example of deictic use of that, very much like the [27ii] example from CGEL (p. 1461):
 i A: Kim has been falsifying the accounts. B: That's terrible. [anaphoric]
ii A: Kim has been falsifying the accounts. B: That's a lie. [discourse-deictic]
In [i] A's utterance is the antecedent for B's that, which refers to the situation that A has described. But in [ii] that refers to A's speech act, to a linguistic entity in the prior discourse.