And now they're carrying unprecedented numbers of passengers
Because, as previously mentioned, they are sending trains in there from railroads that the station was not designed to receive trains from. From the west, NYP was designed to only take PRR trains from their main line, what is now the North Jersey Coast Line, and the former Lehigh Valley RR main line (used to be an engine change at Hunter Interlocking for LVRR). But now the station is hosting trains from the former DL&W Morristown Line, Gladstone Line, Montclair Branch (and even former Erie Greenwood Lake branch), as well as trains that used to run into Grand Central Terminal; and existing NJT trains are having their capacity swollen by people transferring off the Main/Bergen/Pascack Valley lines at Secaucus.
One can only hope that the MTA becomes generous and moves as many LIRR trains out of NYP as soon as they complete their "East Side Access" project to get LIRR trains into Grand Central...but even still, there are voices clamoring to get Metro-North trains into NYP once that happens. Can't keep trying to stuff 10 lbs of sugar into that 5 lb bag.
Unprecedented even from the heyday of the railroads
During the heyday of the railroads, there were four other terminals for passengers to go to. It's a false figure.
The reason the service into Penn is so popular is that it's the fastest way to Midtown for people for whom time is money
Thanks to the lack of capacity at both terminal and on the "High Line", that "fastest way" is getting a lot slower. During peak times, it's actually now faster to ride into Hoboken and get PATH (ferry is not feasible since there is no ferry from Hoboken to Midtown). Yes, it is that bad. Waiting times at Kearny Junction on the former DL&W are excessive, even for reverse-commuting and leisure travel.