Personally, I think if you're changing the appearance of a car to your own personal taste (not necessarily making bespoke parts yourself) and making it go faster than it was intended to, I think that can qualify as being a Hot Rod. Yes, it was of an era where the cars of that era were used and were continued to be used well after they had stopped being made, that was just the fashion. It has evolved, perhaps unwittingly, but in the shape of more modern European and JDM cars.