I buy and sell cars all the time, on modern daily-driver cars it makes a huge difference. Usually the cars have some underlying issue that shows up later, plus the people that deal in junk/salvage/rebuilt title cars are usually junky people often times running some type of scam. I do everything I can to avoid dealing in cars w/ junk titles, but occasionally end up with one.
I have a 2013 Jeep Patriot now with a junk/rebuilt title that I cant give away...its a good running, good driving car, but people are leery of it and I fully understand. On the rare occasion that I have one for sale, I use a full disclosure full transparence approach to selling it...encourage the buyer to have a full inspection done by a qualified mechanic of their chosing, and I list them for sale at .50 cents on the dollar of NADA book value.
Classic and hot rod's are different. The title is just a piece of paper. The classic should be judged on the merits of how it appears now, cosmetically and mechanical. Base your value on the classic itself, not the person selling it or the branded title.
I can't tell you how many big block 4-speed Camaro's there are in the world that started life as a 6 cylinder automatic. Classic Bronco's are in high demand and fetch prices accordingly. A nicely built classic Bronco for a fair price is always a good investment, regardless if it has a branded title....once again, make a fair valuation on the classic itself, NOT the paper work or seller's stories.