I don’t think this is an important factor that makes a big difference, but the identity of the author can make a difference to the value of the comment in the following way.
Consider a correction like the one Zack received on his post about discontinuous linear functions. A reader who sees such a correction from someone they know is good at mathematics can (at least in the absence of further argument about the correction) trust that they got it right, and update their opinions accordingly. If they see such a correction from some rando they know nothing about then they can’t do that, and need to work through the mathematics themself, or wait for someone else to do it, or just put up with not knowing who’s right.
(This is a separate point from the one, already acknowledged by Zack in the OP, that our estimate of comment value may be higher if we know the commenter is expert; I am saying that the actual value of a correct comment is higher if readers know the commenter is expert.)
I don’t think this is an important factor that makes a big difference, but the identity of the author can make a difference to the value of the comment in the following way.
Consider a correction like the one Zack received on his post about discontinuous linear functions. A reader who sees such a correction from someone they know is good at mathematics can (at least in the absence of further argument about the correction) trust that they got it right, and update their opinions accordingly. If they see such a correction from some rando they know nothing about then they can’t do that, and need to work through the mathematics themself, or wait for someone else to do it, or just put up with not knowing who’s right.
(This is a separate point from the one, already acknowledged by Zack in the OP, that our estimate of comment value may be higher if we know the commenter is expert; I am saying that the actual value of a correct comment is higher if readers know the commenter is expert.)