1 - it may look cool: sure it's a more subjective aspect, but the classic appearance of a hot-rod has its fair share of beauty, and it's quite obvious that nowadays a Ford Model A Tudor for instance would stand out of the crowd;
2 - the owner may limit how "modern" the car could be: with so many technical changes within the automotive industry, newer features were becoming more widespread on new vehicles and increasing their complexity. And even though basically every modern body-on-frame pick-up truck may highlight the suitability of such improvements to some older body-on-frame cars, some owners may have their own preferences on how much of such features would be desirable to have, considering most of those were not mandated when the cars more sought after by hot-rodders were originally manufactured;
3 - engine/transmission options may vary: even though the most orthodox definition of a hot-rod has been focused on American V8 engines, with the corresponding toll on fuel-efficiency applying, other engine types can also be fitted. Also considering how a stock 4-cyl engine of a Ford Model A could be souped-up before the small-block V8 engines became mainstream across the Big Three after World War II, even something which could be seen as "unorthodox" such as either a 4-cyl turbocharged gasser or even a turbodiesel could serve just right. And automatic transmissions to improve comfort in town are also not out of question;
4 - crash standards may be less of a concern for some people: sure a modern car with many airbags and crumple zones has its advantages, but not everyone really cares about it. Had some vehicle without airbags and crumple zones not be roadworthy at all, motorcycles would've been forbidden already;
5 - the owner may have the chance to know better the car: unlike newer cars which have been too complex for the average Joe to perform maintenance at home, hot-rods have usually been way more engaging, and their owners more mechanically-inclined and willing to learn all the aspects pertaining to how the car works.