Because they could say it were a private sale, relatives/friends car etc, would make it difficult, if things went wrong. not saying the dealer your talking about is suspect but it does happen.
I don't see that it makes any difference if he uses his home as his base or not. If he's registered and trading as a dealer, he's a dealer. William Loughran & Tom Hartley do the same.
This guy seems to be quite upfront about being a car dealer. He advertises as a car dealer with his full name, address & phone number & appears to have been around a fair while. Google his name.