My current DONE3 was issued by QR. QR had the longest flight on the ticket so the travel agent just sent it to them to ticket automatically.

On my many xONEx's, I've had changes made by QF, JL, AA, BA, CX, MH and AY. AY changed something that MH had screwed up. BA changes things to their benefit (ie, instead of simply changing date on a QF32, they changed it to the BA code as well).
When I asked MH to change something (rather them then just doing it), they told me to go talk to SQ.

Otherwise, changes (or lack of) have very much come down to the agent. Recently (since the US merger), AA agents have tended to get confused, with some saying it can't get changed, others outright refusing, others saying they can't touch it due to different systems, and others simply making the change in a few moments.
When a CX or JL agent has made changes, they have tended to call someone for "permission" then done it. I don't recall any time I've asked JL or CX to make changes and they've refused.
(I've done a yearly RTW since 2006)