This is absolutely not true. The Holy Roman Empire as such was a historic collection of many different empires with different governments and governmental systems. Its history includes being conquered, falling into chaos, and plagued by civil wars. Between many of the different empires and governments laying claim to its name, it often did not even exist in name. Furthermore many of those empires often existed with little authority beyond laying claim to the name. To make a long story short, the Holy Roman Empire did not any time in history exist with continuity as as long as the current U.S. government has existed with continuity.
Historical continuity is indeed a tricky thing. But if you see several Holy Roman Empires of German Nation, then you should also see at least three American republics, in the space of 216 years:
- Pre-Lincoln confederacy in the East
- Expansion into Indian and Mexican territories and robust capitalism
- Wilsonian imperialism and Rooseveltian domestic socialism.