Lots of good information so far in this thread and many interesting scenarios. I think much depends on how old is "old" and what is considered "new". Every situation is unique though and what works for some, may not for all.
I wrestled with this question in the 1970's when I first started my quest for the perfect home. At the time, I lived with my parents in an urban area in a Tudor style house built in the 1920's. Prices, lot sizes and regulations in the area forced me to relocate to the country. I bought 25 acres, lived in a used mobile home, and commuted 75 miles to work while I contemplated what to do about a house.
In my spare time, I helped a friend build his own house and learned a lot about construction. I met a few tradesmen, and with their help & encouragement, decided to build my own as well. I had seen the problems my folks had with the old home where I grew up, which also affected my decision.
I took out a home construction loan using the land as collateral. The building permit was written on the back of a matchbook and with no regulations or building inspections to worry about, it was a fairly easy but lengthy process. Yes, it's easy to get into trouble doing this with no oversight, but with the advice of the tradesmen I met, everything was done right and the way I wanted. I've been living in the house for almost 50 years now and have no regrets.
If I had to start over, IMO, the best approach would be to put up a modular home. There are several companies in this part of the state that let you select your own specs & materials. Some even allow you to inspect the construction process in their factory.