To answer some of the questions, yes, I had the same problem before replacing the pads/rotors (except that there was some grinding from the excessively worn pads).
I did pump the pedal after changing the breaks, and was able to get good pressure on the pedal with the car turned off. The fluid is at the correct level, has never run dry, and I’ve never opened up the system.
I will go ahead with the bleed and get back to you guys…