A few of my friends have consigned nice cars, for a variety of reasons. Some don't have the sales/marketing skills, time or temperament to deal with the process. In many cases, a sizeable amount of money is involved and it is important to ensure buyers are vetted and the funds are properly transferred. Buying/selling a collector car can stir up emotions; having a buffer in the process can keep those in check.
Collector car dealers usually do not have the in-depth knowledge buyers of '60s muscle cars demand. Some take the time to find out. If it is a jack-of-all-trades dealer making "numbers-matching" claims, take them with a grain of salt. Do your homework.
On-line auctions are an alternative. A colleague sold a nice OE drive train Z/28 on BAT last Fall. I had slight involvement to ensure the car was properly described. Someone ended up with a nice car for a very fair price. BAT does a great job of marketing.
Don't assume major auctions are necessarily a great place to buy. I have attended 28 collector car auctions over the years and have seen plenty of mis-represented cars. Repro tags, fake paperwork, even a few rebodies. It is impossible to do an in-depth inspection at those venues. Cars are consigned based on the consignors description; the auction company bears no responsibility for inaccuracy. Buy a mutt and it will be your problem.
One major auction company has made no secret of their intention to de-emphasize old muscle cars.
"...with nine of the top 10 sales falling into the hot categories of Resto-Mods, contemporary supercars, ’80s and ’90s vehicles, and classic trucks and SUVs."