That analysis leaves so many things out of the story that I would hardly even know where to begin pointing out the problems, including ignoring or misunderstanding compound interest (your analysis only holds for someone stuffing dollar bills in their mattress, not under any other feasible holding model across 100 years, which in truth is simply not approximatable in any simplistic fashion anyhow) and the fact that a dollar in the past is intrinsically worth more than a dollar in the present, because the dollar in the past can be leveraged to generate more present wealth. (Typically, this is looked at from the point of view that a dollar in the present is worth more than a dollar in the future and future dollars must be discounted in value when compared to present dollars, but the tense-shifted statement is equivalent, barring the fact that you can't actually spend past-dollars in the past. (In which case a past-dollar would be REALLY valuable...))

Finally, you seem to be claiming that the US (either collectively or per-citizen) is no more wealthy today than it was in 1920 (or 19xx), which is one of those results so absurd that it should be prompting you to reconsider your viewpoint, not prompting you to post on the internet.