There is the same number of Supreme Courts today as there were 200+ years ago, and we have 60 times the population. They are clearly a bottleneck in our legal system, so it's not unreasonable to suggest there should perhaps be 540 SCOTUS Justices in 60 chambers, hearing cases at 60 times the current rate.
You are wrong on a number of points. The Supreme Court originally consisted of six members and the number of members has varied somewhat. It has been at nine for a good number of years. There was no intermediate appellate court. There were simply the trial courts, called circuit courts then, and the Supreme Court. Supreme Court justices were required to ride the circuit, meaning they had to travel many miles and act as trial judges in cases. This constituted the biggest part of their workload for the first hundred years or so.
So, with intermediate appellate courts, no trial court duties, and larger staffs, I'm not sure the actual workload on the justices is really any greater than it has traditionally been. While they (or their staff) may have to review thousands of requests for review, most are clearly not worthy of review and are easily disposed of.