The best AM (and NTSC analog TV is analog AM) detector uses phase-locked-carrier product-detector. Allows tighter filtering and thus better transient/music/video signal recovery. The Motorola MC44301 does this.
The best FM detector may be the Marantz 10B, a vacuum tube FM stereo music receiver, where a front-panel 2" oscilloscope display provides realtime monitoring of multipathing and mis-aligned IF filters and mis-aligned transmitter-receiver carriers. The RF FM is downconverted and amplified and heavily and sharply filtered, and zero-crossings are detected and converted into fast-edge digital pulses. These pulses carry the FM information, and drive a fixed pulse-width (monostable) circuit, the output of which is heavily filtered (Marantz does not say how many poles are used) to provide the recovered information.
Note the presence of frequency-error results in DC output, and a high-pass-filter blocks this. Also note the presence of phase-noise causes slight timing fluctuation of the information-carrying zero-crossings; all oscillators have some phase-noise (aka jitter); if broadband, the human ear is not bothered; if tonal as from 60/120Hz power supply effects, the listener will complain.
However, I've seen circuits for some of the GSM cellphones; these used zero-IF detection, where the receiver oscillator is "on" the Transmitter frequency but with slight frequency error and unknown phase error.
To properly handle these errors, the zero-IF signal (separated into Inphase and Quadrature parts) is digitized and the packet (GSM cellphones use 577 packets per second) training sequence is processed to extract the phase-rotation during that mid-packet known-bit-pattern interval. By examining phase-rotation, and then cancelling the phase-rotation, an adequately phase-constant signal (digital, at this point) is available for data-eye matching against the four phase-patterns allowed in GSM.