I mean even if Barker gave it to Rich, that doesn't necessarily mean that was THE only mic Bob used on the show. It doesn't necessarily mean it was ONE of Barker's mics...it could have been one of several used in that studio for the show.
I think this is important. As far as I'm aware, all the host-used mics at TVC had 100' cables permanently soldered to them. All of Bob's mics had the handle shrink-wrapped with heat shrink tubing from the late '70s until he started using the custom ECM-510 in 1992 because the paint flecks off the handle of an ECM-51 with any sort of use. The one instance I can recall where a host used an ECM-51 with the stock 10' cord was right before Gene Rayburn's custom non-telescoping mic was built in 1978, and you can see him carrying all 10' of cabling up to the XLR connector in all these shows. I believe these episodes are available to watch on-demand on Freevee right now.
I have no doubt in my mind this came from TVC's inventory and probably existed on Stage 33 at some point in its life, but I doubt it was used by Bob. It seems more likely this was a contestant-used mic just going by the cord length and the condition of the handle. Whether that's worth $2,500 to someone is up to them, and as of this writing, it seems worth that to at least one person.