One point I failed to stress in the last 4 post is the need for filtering. It seems to be a common practice to question the need for a choke or capacitor in a detector circuit.
When the crew examines a circuit they seem to lean towards seeking a minimum part count. Sometimes one part will be the life of a circuit and others not so much but still effect the performance.
If you remove the diode the circuit dies, no question. Removing a capacitor may not have as much effect. If you can tune in a station and then move the headset leads to "fine tune" it you probably should not have left out that filter capacitor. The filter will send AF to the headphones and all is well. The inductance in the headset will "smooth" some RF component in the signal but not as efficiently.
Yes the capacitors are there for a purpose.